### 3 Detailed lookup table and classiﬁcation for each ODE

The following table 3 gives the classiﬁcation of each ODE from Maple ODE advisor with a link to each ODE page as well. Clicking on the problem opens a new page that shows the result.

 Table 3:ODE classiﬁcation and performance for each diﬀerential equation # result ODE 1 $$y'(x)=a f(x)$$ [_quadrature] Solution method Separable ODE, Dependent variable missing Maple ✓Mathematica ✓ ODE 2 $$y'(x)=y(x)+x+\sin (x)$$ [[_linear, class A]] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 3 $$y'(x)=x^2+2 y(x)+3 \cosh (x)$$ [[_linear, class A]] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 4 $$y'(x)=a+b x+c y(x)$$ [[_linear, class A]] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 5 $$y'(x)=a \cos (b x+c)+k y(x)$$ [[_linear, class A]] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 6 $$y'(x)=a \sin (b x+c)+k y(x)$$ [[_linear, class A]] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 7 $$y'(x)=a+b e^{k x}+c y(x)$$ [[_linear, class A]] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 8 $$y'(x)=x \left (x^2-y(x)\right )$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 9 $$y'(x)=x \left (a y(x)+e^{-x^2}\right )$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 10 $$y'(x)=x^2 \left (a x^3+b y(x)\right )$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 11 $$y'(x)=a x^n y(x)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 12 $$y'(x)=y(x) \cos (x)+\sin (x) \cos (x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 13 $$y'(x)=y(x) \cos (x)+e^{\sin (x)}$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 14 $$y'(x)=y(x) \cot (x)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 15 $$y'(x)=1-y(x) \cot (x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 16 $$y'(x)=x \csc (x)-y(x) \cot (x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 17 $$y'(x)=y(x) (\cot (x)+2 \csc (2 x))$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 18 $$y'(x)=\sec (x)-y(x) \cot (x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 19 $$y'(x)=y(x) \cot (x)+e^x \sin (x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 20 $$y'(x)+2 y(x) \cot (x)+\csc (x)=0$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 21 $$y'(x)=4 x \csc (x) \sec ^2(x)-2 y(x) \cot (2 x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 22 $$y'(x)=2 \left (\cos (2 x) \cot ^2(x)-y(x) \csc (2 x)\right )$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 23 $$y'(x)=4 x \csc (x) \left (y(x)+\sin ^3(x)\right )$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 24 $$y'(x)=4 x \csc (x) \left (y(x)-\tan ^2(x)+1\right )$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 25 $$y'(x)=y(x) \sec (x)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 26 $$y'(x)+\tan (x)=(1-y(x)) \sec (x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 27 $$y'(x)=y(x) \tan (x)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 28 $$y'(x)=y(x) \tan (x)+\cos (x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 29 $$y'(x)=\cos (x)-y(x) \tan (x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 30 $$y'(x)=\sec (x)-y(x) \tan (x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 31 $$y'(x)=y(x) \tan (x)+\sin (2 x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 32 $$y'(x)=\sin (2 x)-y(x) \tan (x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 33 $$y'(x)=2 y(x) \tan (x)+\sin (x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 34 $$y'(x)=2 (y(x) \tan (2 x)+\sec (2 x)+1)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 35 $$y'(x)=3 y(x) \tan (x)+\csc (x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 36 $$y'(x)=y(x) (a+\sin (\log (x))+\cos (\log (x)))$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 37 $$y'(x)=6 e^{2 x}-y(x) \tanh (x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 38 $$y'(x)=y(x) f'(x)+f(x) f'(x)$$ odeadvisor timed out Solution method Linear ODE Maple ✓Mathematica ✓ ODE 39 $$y'(x)=f(x)+g(x) y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 40 $$y'(x)=x^2-y(x)^2$$ [_Riccati] Solution method Series solution to $$y'(x)=f(x,y(x))$$, case $$f(x,y)$$ analytic Maple ✓Mathematica ✓ ODE 41 $$f(x)^2+y'(x)=f'(x)+y(x)^2$$ odeadvisor timed out Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✗ ODE 42 $$y'(x)-x+1=y(x) (y(x)+x)$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 43 $$y'(x)=(y(x)+x)^2$$ [[_homogeneous, class C], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 44 $$y'(x)=(x-y(x))^2$$ [[_homogeneous, class C], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 45 $$y'(x)=(x-y(x))^2+3 (y(x)-x+1)$$ [[_homogeneous, class C], _Riccati] Solution method Equation linear in the variables, $$y'(x)=f(a+b x+ c y(x))$$ Maple ✓Mathematica ✓ ODE 46 $$y'(x)=-\left (x^2+1\right ) y(x)+y(x)^2+2 x$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 47 $$y'(x)=x \left (x^3+2\right )-\left (2 x^2-y(x)\right ) y(x)$$ [[_1st_order, _with_linear_symmetries], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 48 $$y'(x)=x \left (2-x^3\right )+\left (2 x^2-y(x)\right ) y(x)+1$$ [[_1st_order, _with_linear_symmetries], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 49 $$y'(x)=\cos (x)-y(x) (\sin (x)-y(x))$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 50 $$y'(x)=y(x) (y(x)+\sin (2 x))+\cos (2 x)$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 51 $$y'(x)=x f(x) y(x)+f(x)+y(x)^2$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 52 $$y'(x)=(-4 y(x)+x+3)^2$$ [[_homogeneous, class C], _Riccati] Solution method Equation linear in the variables, $$y'(x)=f(a+b x+ c y(x))$$ Maple ✓Mathematica ✓ ODE 53 $$y'(x)=(9 y(x)+4 x+1)^2$$ [[_homogeneous, class C], _Riccati] Solution method Equation linear in the variables, $$y'(x)=f(a+b x+ c y(x))$$ Maple ✓Mathematica ✓ ODE 54 $$y'(x)=3 \left (a+b y(x)^2+b x\right )$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 55 $$y'(x)=a+b y(x)^2$$ [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓Mathematica ✓ ODE 56 $$y'(x)=a x+b y(x)^2$$ [[_Riccati, _special]] Solution method Riccati ODE, Main form Maple ✓Mathematica ✓ ODE 57 $$y'(x)=a+b x+c y(x)^2$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 58 $$y'(x)=a x^{n-1}+b x^{2 n}+c y(x)^2$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 59 $$y'(x)=a x^2+b y(x)^2$$ [[_Riccati, _special]] Solution method Riccati ODE, Main form Maple ✓Mathematica ✓ ODE 60 $$y'(x)=\text {a0}+\text {a1} y(x)+\text {a2} y(x)^2$$ [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓Mathematica ✓ ODE 61 $$y'(x)=a y(x)+b y(x)^2+f(x)$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✗Mathematica ✗ ODE 62 $$y'(x)=a (x-y(x)) y(x)+1$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 63 $$y'(x)=a y(x)^2+f(x)+g(x) y(x)$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✗Mathematica ✗ ODE 64 $$y'(x)=x y(x) (y(x)+3)$$ [_separable] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 65 $$y'(x)=-x^3+\left (2 x^2+1\right ) y(x)-x y(x)^2-x+1$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 66 $$y'(x)=x \left (x^2 y(x)-y(x)^2+2\right )$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 67 $$y'(x)=-\left ((1-x) y(x)^2\right )+(1-2 x) y(x)+x$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 68 $$y'(x)=a x y(x)^2$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 69 $$y'(x)=x^n \left (a+b y(x)^2\right )$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 70 $$y'(x)=a x^m+b x^n y(x)^2$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 71 $$y'(x)=y(x) (a+b y(x) \cos (k x))$$ [_Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 72 $$y'(x)=\sin (x) \left (2 \sec ^2(x)-y(x)\right )$$ [_linear] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 73 $$y'(x)+4 \csc (x)=y(x)^2 \sin (x)+y(x) (3-\cot (x))$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 74 $$y'(x)=y(x) \sec (x)+(\sin (x)-1)^2$$ [_linear] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 75 $$y'(x)+\left (1-y(x)^2\right ) \tan (x)=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 76 $$y'(x)=f(x)+g(x) y(x)+h(x) y(x)^2$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✗Mathematica ✗ ODE 77 $$y'(x)=f(x) \left (a+b y(x)+c y(x)^2\right )$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 78 $$y(x)^2 (a x+y(x))+y'(x)$$ [_Abel] Solution method Abel ODE, First kind Maple ✓Mathematica ✗ ODE 79 $$y'(x)=y(x)^2 \left (a e^x+y(x)\right )$$ [_Abel] Solution method Abel ODE, First kind Maple ✓Mathematica ✓ ODE 80 $$3 a (y(x)+2 x) y(x)^2+y'(x)=0$$ [_Abel] Solution method Abel ODE, First kind Maple ✓Mathematica ✓ ODE 81 $$y'(x)=y(x) \left (a+b y(x)^2\right )$$ [_quadrature] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 82 $$y'(x)=\text {a0}+\text {a1} y(x)+\text {a2} y(x)^2+\text {a3} y(x)^3$$ [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓Mathematica ✓ ODE 83 $$y'(x)=x y(x)^3$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 84 $$y'(x)+y(x) \left (1-x y(x)^2\right )=0$$ [_Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 85 $$y'(x)=y(x)^2 (a+b x y(x))$$ [[_homogeneous, class G], _Abel] Solution method Abel ODE, First kind Maple ✓Mathematica ✓ ODE 86 $$y(x)^3 \left (a+4 b^2 x+3 b x^2\right )+y'(x)+3 x y(x)^2=0$$ [_Abel] Solution method Abel ODE, First kind Maple ✓Mathematica ✓ ODE 87 $$y'(x)=y(x)^2 \left (x^3 y(x)+1\right )$$ [_Abel] Solution method Abel ODE, First kind Maple ✗Mathematica ✗ ODE 88 $$2 x y(x) \left (a x y(x)^2+1\right )+y'(x)=0$$ [_Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 89 $$y'(x)=y(x)^2-a x \left (1-x^{n-1}\right ) y(x)^3$$ [_Abel] Solution method Abel ODE, First kind Maple ✗Mathematica ✗ ODE 90 $$y'(x)=a y(x)^2+x y(x)^3 \left (b+c x^{n-1}\right )$$ [_Abel] Solution method Abel ODE, First kind Maple ✗Mathematica ✗ ODE 91 $$y'(x)+y(x) \left (y(x)^2 \sec (x)+\tan (x)\right )=0$$ [_Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 92 $$y'(x)+y(x)^3 \tan (x) \sec (x)=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 93 $$y'(x)=\text {f0}(x)+\text {f1}(x) y(x)+\text {f2}(x) y(x)^2+\text {f3}(x) y(x)^3$$ [_Abel] Solution method Abel ODE, First kind Maple ✗Mathematica ✗ ODE 94 $$y'(x)=y(x) \left (y(x)^3 \sec (x)+\tan (x)\right )$$ [_Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 95 $$y'(x)=a x^{\frac {n}{1-n}}+b y(x)^n$$ [[_homogeneous, class G], _Chini] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 96 $$y'(x)=f(x) y(x)+g(x) y(x)^k$$ [_Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 97 $$y'(x)=f(x)+g(x) y(x)+h(x) y(x)^n$$ [_Chini] Solution method Change of Variable, new dependent variable Maple ✗Mathematica ✗ ODE 98 $$y'(x)=f(x) y(x)^m+g(x) y(x)^n$$ [NONE] Solution method Change of Variable, new dependent variable Maple ✗Mathematica ✗ ODE 99 $$y'(x)=\sqrt {| y(x)| }$$ [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓Mathematica ✓ ODE 100 $$y'(x)=a+\sqrt {\text {A0}+\text {B0} y(x)}+b y(x)$$ [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓Mathematica ✓ ODE 101 $$y'(x)=a x+b \sqrt {y(x)}$$ [[_homogeneous, class G], _Chini] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 102 $$x^3+y'(x)=x \sqrt {x^4+4 y(x)}$$ [[_1st_order, _with_linear_symmetries]] Solution method Homogeneous equation, isobaric equation Maple ✓Mathematica ✓ ODE 103 $$y'(x)+2 \left (1-x \sqrt {y(x)}\right ) y(x)=0$$ [_Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 104 $$y'(x)=\sqrt {a+b y(x)^2}$$ [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓Mathematica ✓ ODE 105 $$y'(x)=y(x) \sqrt {a+b y(x)}$$ [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓Mathematica ✓ ODE 106 $$g(x) (f(x)-y(x)) \sqrt {(y(x)-a) (y(x)-b)}+y'(x)=0$$ [y=_G(x,y')] Solution method Change of Variable, new dependent variable Maple ✗Mathematica ✗ ODE 107 $$y'(x)=\sqrt {X Y}$$ [_quadrature] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 108 $$y'(x)=\text {R1}\left (x,\sqrt {X}\right ) \text {R2}\left (y(x),\sqrt {Y}\right )$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 109 $$y'(x)=\cos ^2(x) \cos (y(x))$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 110 $$y'(x)=\sec ^2(x) \text {Cosy}(y(x)) \cot (y(x))$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 111 $$y'(x)=a+b \cos (A x+B y(x))$$ [[_homogeneous, class C], _dAlembert] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 112 $$y'(x)=-\left (1-f'(x)\right ) \cos (y(x))+f'(x)-f(x) \sin (y(x))+1$$ odeadvisor timed out Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 113 $$g(x) \sin (a y(x))+h(x) \cos (a y(x))+f(x)+y'(x)=0$$ [y=_G(x,y')] Solution method Change of Variable, new dependent variable Maple ✗Mathematica ✗ ODE 114 $$y'(x)=a+b \cos (y(x))$$ [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓Mathematica ✓ ODE 115 $$x \left (\sin (2 y(x))-x^2 \cos ^2(y(x))\right )+y'(x)=0$$ [y=_G(x,y')] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 116 $$y'(x)+\tan (x) \sec (x) \cos ^2(y(x))=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 117 $$y'(x)=\cot (x) \cot (y(x))$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 118 $$y'(x)+\cot (x) \cot (y(x))=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 119 $$y'(x)=\sin (x) (\csc (y(x))-\cot (y(x)))$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 120 $$y'(x)=\tan (x) \cot (y(x))$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 121 $$y'(x)+\tan (x) \cot (y(x))=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 122 $$y'(x)+\sin (2 x) \csc (2 y(x))=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 123 $$y'(x)=\tan (x) (\tan (y(x))+\sec (x) \sec (y(x)))$$ [y=_G(x,y')] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 124 $$y'(x)=\cos (x) \sec ^2(y(x))$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 125 $$y'(x)=\sec ^2(x) \sec ^3(y(x))$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 126 $$y'(x)=a+b \sin (y(x))$$ [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓Mathematica ✓ ODE 127 $$y'(x)=a+b \sin (A x+B y(x))$$ [[_homogeneous, class C], _dAlembert] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 128 $$y'(x)=\tan (y(x)) (\cos (x) \sin (y(x))+1)$$ [y=_G(x,y')] Solution method Change of Variable, new dependent variable Maple ✗Mathematica ✓ ODE 129 $$y'(x)+\csc (2 x) \sin (2 y(x))=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 130 $$f(x)+g(x) \tan (y(x))+y'(x)=0$$ [y=_G(x,y')] Solution method Change of Variable, new dependent variable Maple ✗Mathematica ✗ ODE 131 $$y'(x)=\sqrt {a+b \cos (y(x))}$$ [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓Mathematica ✓ ODE 132 $$y'(x)=e^{y(x)}+x$$ [[_1st_order, _with_symmetry_[F(x),G(x)]]] Solution method Series solution to $$y'(x)=f(x,y(x))$$, case $$f(x,y)$$ analytic Maple ✓Mathematica ✓ ODE 133 $$y'(x)=e^{y(x)+x}$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 134 $$y'(x)=e^x \left (a+b e^{-y(x)}\right )$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 135 $$y'(x)+y(x) \log (x) \log (y(x))=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 136 $$y'(x)=x^{m-1} y(x)^{1-n} f\left (a x^m+b y(x)^n\right )$$ [[_1st_order, _with_symmetry_[F(x),G(y)]]] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 137 $$y'(x)=a f(y(x))$$ [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓Mathematica ✓ ODE 138 $$y'(x)=f(a+b x+c y(x))$$ [[_homogeneous, class C], _dAlembert] Solution method Equation linear in the variables, $$y'(x)=f(a+b x+ c y(x))$$ Maple ✓Mathematica ✓ ODE 139 $$y'(x)=f(x) g(y(x))$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 140 $$y'(x)=\text {Csx}(x) y(x) \sec (x)+\sec ^2(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 141 $$2 y'(x)+2 \csc ^2(x)=y(x) \csc (x) \sec (x)-y(x)^2 \sec ^2(x)$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 142 $$2 y'(x)=2 \sin ^2(y(x)) \tan (y(x))-x \sin (2 y(x))$$ [y=_G(x,y')] Solution method Change of Variable, new dependent variable Maple ✗Mathematica ✓ ODE 143 $$a x+2 y'(x)=\sqrt {a^2 x^2-4 b x^2-4 c y(x)}$$ [[_homogeneous, class G]] Solution method Homogeneous equation, isobaric equation Maple ✓Mathematica ✓ ODE 144 $$3 y'(x)=\sqrt {x^2-3 y(x)}+x$$ [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 145 $$x y'(x)=\sqrt {a^2-x^2}$$ [_quadrature] Solution method Separable ODE, Dependent variable missing Maple ✓Mathematica ✓ ODE 146 $$x y'(x)+y(x)+x=0$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 147 $$x^2+x y'(x)-y(x)=0$$ [_linear] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 148 $$x y'(x)=x^3-y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 149 $$x y'(x)=x^3+y(x)+1$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 150 $$x y'(x)=x^m+y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 151 $$x y'(x)=x \sin (x)-y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 152 $$x y'(x)=x^2 \sin (x)+y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 153 $$x y'(x)=x^n \log (x)-y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 154 $$x y'(x)=\sin (x)-2 y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 155 $$x y'(x)=a y(x)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 156 $$x y'(x)=a y(x)+x+1$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 157 $$x y'(x)=a x+b y(x)$$ [_linear] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 158 $$x y'(x)=a x^2+b y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 159 $$x y'(x)=a+b x^n+c y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 160 $$x y'(x)+(3-x) y(x)+2=0$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 161 $$(a x+2) y(x)+x y'(x)+x=0$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 162 $$y(x) (a+b x)+x y'(x)=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 163 $$x y'(x)=x^3+\left (1-2 x^2\right ) y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 164 $$x y'(x)=a x-\left (1-b x^2\right ) y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 165 $$\left (2-a x^2\right ) y(x)+x y'(x)+x=0$$ [_linear] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 166 $$x^2+x y'(x)+y(x)^2=0$$ [_rational, _Riccati] Solution method Riccati ODE, Special cases Maple ✓Mathematica ✓ ODE 167 $$x y'(x)=x^2+y(x) (y(x)+1)$$ [[_homogeneous, class D], _rational, _Riccati] Solution method Riccati ODE, Special cases Maple ✓Mathematica ✓ ODE 168 $$x y'(x)+y(x)^2-y(x)=x^{2/3}$$ [_rational, _Riccati] Solution method Riccati ODE, Special cases Maple ✓Mathematica ✓ ODE 169 $$x y'(x)=a+b y(x)^2$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 170 $$x y'(x)=a x^2+b y(x)^2+y(x)$$ [[_homogeneous, class D], _rational, _Riccati] Solution method Riccati ODE, Special cases Maple ✓Mathematica ✓ ODE 171 $$x y'(x)=a x^{2 n}+y(x) (b y(x)+n)$$ [_rational, _Riccati] Solution method Riccati ODE, Special cases Maple ✓Mathematica ✓ ODE 172 $$x y'(x)=a x^n+b y(x)+c y(x)^2$$ [_rational, _Riccati] Solution method Riccati ODE, Special cases Maple ✓Mathematica ✓ ODE 173 $$x y'(x)=a x^n+b y(x)+c y(x)^2+k$$ [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 174 $$a+x y'(x)+x y(x)^2=0$$ [_rational, [_Riccati, _special]] Solution method Riccati ODE, Main form Maple ✓Mathematica ✓ ODE 175 $$x y'(x)+y(x) (1-x y(x))=0$$ [[_homogeneous, class G], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 176 $$x y'(x)=y(x) (1-x y(x))$$ [[_homogeneous, class D], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 177 $$x y'(x)=y(x) (x y(x)+1)$$ [[_homogeneous, class D], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 178 $$x y'(x)=a x^3 y(x) (1-x y(x))$$ [_Bernoulli] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 179 $$x y'(x)=x^3+\left (2 x^2+1\right ) y(x)+x y(x)^2$$ [[_homogeneous, class D], _rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 180 $$x y'(x)=y(x) (2 x y(x)+1)$$ [[_homogeneous, class D], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 181 $$y(x) (a x y(x)+2)+b x+x y'(x)=0$$ [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 182 $$\text {a0}+\text {a1} x+y(x) (\text {a2}+\text {a3} x y(x))+x y'(x)=0$$ [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 183 $$a x^2 y(x)^2+x y'(x)+2 y(x)=b$$ [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 184 $$\frac {1}{2} (n-m) y(x)+x^m+x^n y(x)^2+x y'(x)=0$$ [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 185 $$y(x) \left (a+b x^n y(x)\right )+x y'(x)=0$$ [[_homogeneous, class G], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 186 $$x y'(x)=a x^m-b y(x)-c x^n y(x)^2$$ [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 187 $$x y'(x)=a x^n (x-y(x))^2-y(x)+2 x$$ [[_1st_order, _with_linear_symmetries], _rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 188 $$y(x) (1-a y(x) \log (x))+x y'(x)=0$$ [_Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 189 $$x y'(x)=f(x) \left (x^2-y(x)^2\right )+y(x)$$ [[_homogeneous, class D], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 190 $$x y'(x)=y(x) \left (y(x)^2+1\right )$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 191 $$x y'(x)+y(x) \left (1-x y(x)^2\right )=0$$ [[_homogeneous, class G], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 192 $$x y'(x)+y(x)=a \left (x^2+1\right ) y(x)^3$$ [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 193 $$x y'(x)=a y(x)+b \left (x^2+1\right ) y(x)^3$$ [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 194 $$x y'(x)+2 y(x)=a x^{2 k} y(x)^k$$ [[_homogeneous, class G], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 195 $$x y'(x)=4 \left (y(x)-\sqrt {y(x)}\right )$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 196 $$x y'(x)+2 y(x)=\sqrt {y(x)^2+1}$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 197 $$x y'(x)=\sqrt {x^2+y(x)^2}+y(x)$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 198 $$x y'(x)=\sqrt {x^2-y(x)^2}+y(x)$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 199 $$x y'(x)=x \sqrt {x^2+y(x)^2}+y(x)$$ [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] Solution method Homogeneous equation, $$xy'(x)=x f(x) g(u)+y(x)$$ Maple ✓Mathematica ✓ ODE 200 $$x y'(x)=y(x)-x (x-y(x)) \sqrt {x^2+y(x)^2}$$ [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] Solution method Homogeneous equation, $$xy'(x)=x f(x) g(u)+y(x)$$ Maple ✓Mathematica ✓ ODE 201 $$x y'(x)=a \sqrt {b^2 x^2+y(x)^2}+y(x)$$ [[_homogeneous, class A], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 202 $$\cos (y(x)) \left (\sin (y(x))-3 x^2 \cos (y(x))\right )+x y'(x)=0$$ [y=_G(x,y')] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 203 $$x y'(x)-y(x)+x \cos \left (\frac {y(x)}{x}\right )+x=0$$ [[_homogeneous, class A], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 204 $$x y'(x)=y(x)-x \cos ^2\left (\frac {y(x)}{x}\right )$$ [[_homogeneous, class A], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 205 $$x y'(x)=\left (1-2 x^2\right ) \cot ^2(y(x))$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 206 $$x y'(x)=y(x)-\cot ^2(y(x))$$ [_separable] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 207 $$x y'(x)+y(x)+2 x \sec (x y(x))=0$$ [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 208 $$x y'(x)-y(x)+x \sec \left (\frac {y(x)}{x}\right )=0$$ [[_homogeneous, class A], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 209 $$x y'(x)=y(x)+x \sec ^2\left (\frac {y(x)}{x}\right )$$ [[_homogeneous, class A], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 210 $$x y'(x)=\sin (x-y(x))$$ [y=_G(x,y')] Solution method Change of Variable, new dependent variable Maple ✗Mathematica ✗ ODE 211 $$x y'(x)=y(x)+x \sin \left (\frac {y(x)}{x}\right )$$ [[_homogeneous, class A], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 212 $$x y'(x)+\tan (y(x))=0$$ [_separable] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 213 $$x y'(x)+\tan (y(x)+x)+x=0$$ [[_1st_order, _with_linear_symmetries]] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 214 $$x y'(x)=y(x)-x \tan \left (\frac {y(x)}{x}\right )$$ [[_homogeneous, class A], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 215 $$x y'(x)=\left (y(x)^2+1\right ) \left (x^2+\tan ^{-1}(y(x))\right )$$ [y=_G(x,y')] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 216 $$x y'(x)=x e^{\frac {y(x)}{x}}+y(x)$$ [[_homogeneous, class A], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 217 $$x y'(x)=x e^{\frac {y(x)}{x}}+y(x)+x$$ [[_homogeneous, class A], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 218 $$x y'(x)=y(x) \log (y(x))$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 219 $$x y'(x)=y(x) (-\log (y(x))+\log (x)+1)$$ [[_homogeneous, class A], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 220 $$x y'(x)+y(x) (-\log (y(x))-\log (x)+1)=0$$ [[_homogeneous, class G]] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 221 $$x y'(x)=y(x)-2 x \tanh \left (\frac {y(x)}{x}\right )$$ [[_homogeneous, class A], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 222 $$n y(x)+x y'(x)=f(x) g\left (x^n y(x)\right )$$ [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 223 $$x y'(x)=y(x) f\left (x^m y(x)^n\right )$$ [[_homogeneous, class G]] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 224 $$(x+1) y'(x)=(3 x+4) x^3+y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 225 $$(x+1) y'(x)=2 y(x)+(x+1)^4$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 226 $$(x+1) y'(x)=n y(x)+e^x (x+1)^{n+1}$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 227 $$(x+1) y'(x)=a y(x)+b x y(x)^2$$ [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 228 $$(x+1) y'(x)+(x+1)^4 y(x)^3+y(x)=0$$ [[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 229 $$(x+1) y'(x)=y(x) \left (1-x y(x)^3\right )$$ [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 230 $$(x+1) y'(x)=(x+1) \sqrt {y(x)+1}+y(x)+1$$ [[_1st_order, _with_linear_symmetries]] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 231 $$(a+x) y'(x)=b x$$ [_quadrature] Solution method Separable ODE, Dependent variable missing Maple ✓Mathematica ✓ ODE 232 $$(a+x) y'(x)=b x+y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 233 $$(a+x) y'(x)+b x^2+y(x)=0$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 234 $$(a+x) y'(x)=2 (a+x)^5+3 y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 235 $$(a+x) y'(x)=b+c y(x)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 236 $$(a+x) y'(x)=b x+c y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 237 $$(a+x) y'(x)=y(x) (1-a y(x))$$ [_separable] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 238 $$(a-x) y'(x)=y(x)^3 (b+c x)+y(x)$$ [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 239 $$2 x y'(x)=2 x^3-y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 240 $$2 x y'(x)+1=y(x)^2+4 i x y(x)$$ [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 241 $$2 x y'(x)=y(x) \left (y(x)^2+1\right )$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 242 $$2 x y'(x)+y(x) \left (y(x)^2+1\right )=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 243 $$2 x y'(x)=y(x) \left (-6 y(x)^2+x+1\right )$$ [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 244 $$\sqrt {a^2-4 b-4 c y(x)}+a+2 x y'(x)+4 y(x)=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 245 $$(1-2 x) y'(x)=2 (-3 y(x)+16 x+8)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 246 $$(2 x+1) y'(x)=4 e^{-y(x)}-2$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 247 $$2 (1-x) y'(x)=y(x)+4 \sqrt {1-x} x$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 248 $$2 (x+1) y'(x)+(x+1)^4 y(x)^3+2 y(x)=0$$ [[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 249 $$3 x y'(x)=3 x^{2/3}+(1-3 y(x)) y(x)$$ [_rational, _Riccati] Solution method Riccati ODE, Special cases Maple ✓Mathematica ✓ ODE 250 $$3 x y'(x)=y(x) \left (x y(x)^3+2\right )$$ [[_homogeneous, class G], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 251 $$3 x y'(x)=y(x) \left (3 x y(x)^3 \log (x)+1\right )$$ [_Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 252 $$x^2 y'(x)=a-y(x)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 253 $$x^2 y'(x)=a+b x+c x^2+x y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 254 $$x^2 y'(x)=a+b x+c x^2-x y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 255 $$x^2 y'(x)+(1-2 x) y(x)=x^2$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 256 $$x^2 y'(x)=a+b x y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 257 $$x^2 y'(x)=y(x) (a+b x)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 258 $$x^2 y'(x)+(x+2) x y(x)=\left (1-e^{-2 x}\right ) x-2$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 259 $$x^2 y'(x)+2 (1-x) x y(x)=e^x \left (2 e^x-1\right )$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 260 $$x^2 y'(x)+x^2+x y(x)+y(x)^2=0$$ [[_homogeneous, class A], _rational, _Riccati] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 261 $$x^2 y'(x)=(-y(x)+2 x+1)^2$$ [[_homogeneous, class C], _rational, _Riccati] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 262 $$x^2 y'(x)=a+b y(x)^2$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 263 $$x^2 y'(x)=y(x) (a y(x)+x)$$ [[_homogeneous, class A], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 264 $$x^2 y'(x)=y(x) (a x+b y(x))$$ [[_homogeneous, class A], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 265 $$a x^2+b x y(x)+c y(x)^2+x^2 y'(x)=0$$ [[_homogeneous, class A], _rational, _Riccati] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 266 $$x^2 y'(x)=a+b x^n+x^2 y(x)^2$$ [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 267 $$x^2 y'(x)+x y(x) (x y(x)+4)+2=0$$ [[_homogeneous, class G], _rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 268 $$a x (1-x y(x))+x^2 y'(x)+x^2 \left (-y(x)^2\right )+2=0$$ [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 269 $$x^2 y'(x)=a+b x^2 y(x)^2$$ [[_homogeneous, class G], _rational, [_Riccati, _special]] Solution method Riccati ODE, Main form Maple ✓Mathematica ✓ ODE 270 $$x^2 y'(x)=a+b x^n+c x^2 y(x)^2$$ [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 271 $$x^2 y'(x)=a+b x y(x)+c x^2 y(x)^2$$ [[_homogeneous, class G], _rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 272 $$x^2 y'(x)=a+b x y(x)+c x^4 y(x)^2$$ [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 273 $$x^2 y'(x)+y(x) \left (x^2+y(x)^2-x\right )=0$$ [[_homogeneous, class D], _rational, _Bernoulli] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 274 $$x^2 y'(x)=2 y(x) \left (x-y(x)^2\right )$$ [[_homogeneous, class G], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 275 $$x^2 y'(x)=a x^2 y(x)^2-a y(x)^3$$ [_rational, _Abel] Solution method Abel ODE, Second kind Maple ✓Mathematica ✓ ODE 276 $$a y(x)^2+b x^2 y(x)^3+x^2 y'(x)=0$$ [_rational, _Abel] Solution method Abel ODE, Second kind Maple ✓Mathematica ✓ ODE 277 $$x^2 y'(x)=y(x) \left (a x+b y(x)^3\right )$$ [[_homogeneous, class G], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 278 $$x^2 y'(x)+x y(x)+\sqrt {y(x)}=0$$ [[_homogeneous, class G], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 279 $$x^2 y'(x)=3 x \tan (y(x))+\sec (y(x))$$ [y=_G(x,y')] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 280 $$\left (1-x^2\right ) y'(x)=-x^2+y(x)+1$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 281 $$\left (1-x^2\right ) y'(x)+1=x y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 282 $$\left (1-x^2\right ) y'(x)=5-x y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 283 $$a+\left (x^2+1\right ) y'(x)+x y(x)=0$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 284 $$a+\left (x^2+1\right ) y'(x)-x y(x)=0$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 285 $$a+\left (1-x^2\right ) y'(x)-x y(x)=0$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 286 $$\left (1-x^2\right ) y'(x)+x y(x)-x=0$$ [_separable] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 287 $$\left (1-x^2\right ) y'(x)-x^2+x y(x)=0$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 288 $$\left (1-x^2\right ) y'(x)+x^2+x y(x)=0$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 289 $$\left (x^2+1\right ) y'(x)=x \left (x^2+1\right )-x y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 290 $$\left (x^2+1\right ) y'(x)=x \left (3 x^2-y(x)\right )$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 291 $$\left (1-x^2\right ) y'(x)+2 x y(x)=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 292 $$\left (x^2+1\right ) y'(x)=2 x (x-y(x))$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 293 $$\left (x^2+1\right ) y'(x)=2 x \left (x^2+1\right )^2+2 x y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 294 $$\left (1-x^2\right ) y'(x)+\cos (x)=2 x y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 295 $$\left (x^2+1\right ) y'(x)=\tan (x)-2 x y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 296 $$\left (1-x^2\right ) y'(x)=a+4 x y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 297 $$\left (x^2+1\right ) y'(x)=y(x) (a+2 b x)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 298 $$\left (x^2+1\right ) y'(x)=y(x)^2+1$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 299 $$\left (1-x^2\right ) y'(x)=1-y(x)^2$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 300 $$\left (1-x^2\right ) y'(x)=1-(2 x-y(x)) y(x)$$ [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 301 $$\left (1-x^2\right ) y'(x)=n \left (y(x)^2-2 x y(x)+1\right )$$ [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 302 $$\left (x^2+1\right ) y'(x)+x (1-y(x)) y(x)=0$$ [_separable] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 303 $$\left (1-x^2\right ) y'(x)=x y(x) (a y(x)+1)$$ [_separable] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 304 $$\left (x^2+1\right ) y'(x)=y(x)^2-2 x \left (y(x)^2+1\right ) y(x)+1$$ [_rational, _Abel] Solution method Abel ODE, Second kind Maple ✓Mathematica ✓ ODE 305 $$\left (x^2+1\right ) y'(x)+x \sin (y(x)) \cos (y(x))=x \left (x^2+1\right ) \cos ^2(y(x))$$ [y=_G(x,y')] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 306 $$\left (x^2+1\right ) y'(x)=x^2-y(x) \cot ^{-1}(x)+1$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 307 $$\left (4-x^2\right ) y'(x)+4 y(x)=(x+2) y(x)^2$$ [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 308 $$\left (a^2+x^2\right ) y'(x)=b+x y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 309 $$\left (a^2+x^2\right ) y'(x)=\left (\sqrt {a^2+x^2}+x\right ) (b+y(x))$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 310 $$\left (a^2+x^2\right ) y'(x)+(x-y(x)) y(x)=0$$ [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 311 $$\left (a^2+x^2\right ) y'(x)=a^2-2 y(x)^2+3 x y(x)$$ [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 312 $$\left (a^2+x^2\right ) y'(x)+b x y(x)^2+x y(x)=0$$ [_separable] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 313 $$(1-x) x y'(x)=a+(x+1) y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 314 $$(1-x) x y'(x)=2 (x y(x)+1)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 315 $$(1-x) x y'(x)=2 (x y(x)-1)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 316 $$x (x+1) y'(x)=(1-2 x) y(x)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 317 $$(1-x) x y'(x)+(2 x+1) y(x)=a$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 318 $$(1-x) x y'(x)=a+2 (2-x) y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 319 $$(1-x) x y'(x)-3 x y(x)+y(x)+2=0$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 320 $$x (x+1) y'(x)=\left (x^2+x-1\right ) y(x)+(x+1) \left (x^2-1\right )$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 321 $$x^2+(x-3) (x-2) y'(x)+3 x y(x)-8 y(x)=0$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 322 $$x (a+x) y'(x)=y(x) (b+c y(x))$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 323 $$(a+x)^2 y'(x)=2 (a+x) (b+y(x))$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 324 $$k (-a+y(x)+x)^2+(x-a)^2 y'(x)+y(x)^2=0$$ [[_homogeneous, class C], _rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 325 $$(x-a) (x-b) y'(x)+k y(x)=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 326 $$(x-a) (x-b) y'(x)=y(x) (-a-b+2 x)+(x-a) (x-b)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 327 $$(x-a) (x-b) y'(x)=c y(x)^2$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 328 $$k (y(x)-a) (y(x)-b)+(x-a) (x-b) y'(x)=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 329 $$k (-a+y(x)+x) (-b+y(x)+x)+(x-a) (x-b) y'(x)+y(x)^2=0$$ [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 330 $$2 x^2 y'(x)=y(x)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 331 $$2 x^2 y'(x)+2 x^2 y(x) \cot (x)+x \cot (x)-1=0$$ [_linear] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 332 $$2 x^2 y'(x)+x^2 \left (-y(x)^2\right )+2 x y(x)+1=0$$ [[_homogeneous, class G], _rational, _Riccati] Solution method Homogeneous equation, isobaric equation Maple ✓Mathematica ✓ ODE 333 $$2 x^2 y'(x)=\left (x^2-y(x)^2\right ) (1-x \cot (x))+2 x y(x)$$ [[_homogeneous, class D], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 334 $$2 \left (1-x^2\right ) y'(x)=\sqrt {1-x^2}+(x+1) y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 335 $$(1-2 x) x y'(x)+(1-4 x) y(x)+1=0$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 336 $$(1-2 x) x y'(x)=y(x)^2-(4 x+1) y(x)+4 x$$ [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 337 $$2 (1-x) x y'(x)+(1-2 x) y(x)+x=0$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 338 $$2 (1-x) x y'(x)+(1-x) y(x)^2+x=0$$ [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 339 $$2 \left (x^2+x+1\right ) y'(x)=8 x^2-(2 x+1) y(x)+1$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 340 $$4 \left (x^2+1\right ) y'(x)-x^2-4 x y(x)=0$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 341 $$a x^2 y'(x)=a x y(x)+b^2 y(x)^2+x^2$$ [[_homogeneous, class A], _rational, _Riccati] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 342 $$\left (a+b x^2\right ) y'(x)=A+B y(x)^2$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 343 $$\left (a+b x^2\right ) y'(x)=c x y(x) \log (y(x))$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 344 $$x (a x+1) y'(x)+a-y(x)=0$$ [_separable] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 345 $$(a+b x)^2 y'(x)+y(x)^3 (a+b x)+c y(x)^2=0$$ [_rational, _Abel] Solution method Abel ODE, Second kind Maple ✓Mathematica ✓ ODE 346 $$x^3 y'(x)=a+b x^2 y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 347 $$x^3 y'(x)=x^2 y(x)-x^2+3$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 348 $$x^3 y'(x)=x^4+y(x)^2$$ [[_homogeneous, class G], _rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 349 $$x^3 y'(x)=y(x) \left (x^2+y(x)\right )$$ [[_homogeneous, class D], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 350 $$x^3 y'(x)=x^2 (y(x)-1)+y(x)^2$$ [[_homogeneous, class D], _rational, _Riccati] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 351 $$x^3 y'(x)=(x+1) y(x)^2$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 352 $$x^3 y'(x)+x^2 y(x) \left (1-x^2 y(x)\right )+20=0$$ [[_homogeneous, class G], _rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 353 $$x^6 \left (-y(x)^2\right )+x^3 y'(x)+(3-2 x) x^2 y(x)+3=0$$ [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 354 $$x^3 y'(x)=y(x) \left (2 x^2+y(x)^2\right )$$ [[_homogeneous, class A], _rational, _Bernoulli] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 355 $$x^3 y'(x)=\cos (y(x)) \left (\cos (y(x))-2 x^2 \sin (y(x))\right )$$ [y=_G(x,y')] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 356 $$x \left (x^2+1\right ) y'(x)=a x^2+y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 357 $$x \left (1-x^2\right ) y'(x)=a x^2+y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 358 $$x \left (x^2+1\right ) y'(x)=a x^3+y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 359 $$x \left (x^2+1\right ) y'(x)=a-x^2 y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 360 $$x \left (x^2+1\right ) y'(x)=\left (1-x^2\right ) y(x)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 361 $$x \left (1-x^2\right ) y'(x)=\left (x^2-x+1\right ) y(x)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 362 $$x \left (1-x^2\right ) y'(x)=a x^3+\left (1-2 x^2\right ) y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 363 $$x \left (1-x^2\right ) y'(x)=\left (1-2 x^2\right ) y(x)+\left (1-x^2\right ) x^3$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 364 $$x \left (x^2+1\right ) y'(x)=2 \left (1-2 x^2 y(x)\right )$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 365 $$x \left (x^2+1\right ) y'(x)=x-\left (5 x^2+3\right ) y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 366 $$\left (1-x^2\right ) x y'(x)+\left (1-x^2\right ) y(x)^2+x^2=0$$ [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 367 $$(1-x) x^2 y'(x)=(2-x) x y(x)-y(x)^2$$ [[_homogeneous, class D], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 368 $$2 x^3 y'(x)=y(x) \left (x^2-y(x)^2\right )$$ [[_homogeneous, class A], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 369 $$2 x^3 y'(x)=y(x) \left (a y(x)^2+3 x^2\right )$$ [[_homogeneous, class A], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 370 $$6 x^3 y'(x)=4 x^2 y(x)+(1-3 x) y(x)^4$$ [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 371 $$x y'(x) \left (a+b x+c x^2\right )-y(x) \left (a+b x+c x^2\right )+x^2=y(x)^2$$ [[_homogeneous, class D], _rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 372 $$x^4 y'(x)=y(x) \left (x^3+y(x)\right )$$ [[_homogeneous, class D], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 373 $$a^2+x^4 y'(x)+x^4 y(x)^2=0$$ [_rational, [_Riccati, _special]] Solution method Riccati ODE, Main form Maple ✓Mathematica ✓ ODE 374 $$x^4 y'(x)+x^3 y(x)+\csc (x y(x))=0$$ [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 375 $$\left (1-x^4\right ) y'(x)=2 x \left (1-y(x)^2\right )$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 376 $$x \left (1-x^3\right ) y'(x)=2 x-\left (1-4 x^3\right ) y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 377 $$x \left (1-x^3\right ) y'(x)=x^2+y(x) (1-2 x y(x))$$ [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 378 $$x^2 \left (1-x^2\right ) y'(x)=y(x) \left (x-3 x^3 y(x)\right )$$ [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 379 $$x \left (1-2 x^3\right ) y'(x)=2 \left (1-x^3\right ) y(x)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 380 $$\left (y'(x)+y(x)^2\right ) \left (a+b x+c x^2\right )^2+A=0$$ [_rational, _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 381 $$x^5 y'(x)=1-3 x^4 y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 382 $$x \left (1-x^4\right ) y'(x)=\left (1-x^4\right ) y(x)+2 x \left (x^2-y(x)^2\right )$$ [[_homogeneous, class D], _rational, _Riccati] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 383 $$x^7 y'(x)+5 x^3 y(x)^2+2 \left (x^2+1\right ) y(x)^3=0$$ [_rational, _Abel] Solution method Abel ODE, First kind Maple ✓Mathematica ✓ ODE 384 $$x^n y'(x)=a+b x^{n-1} y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 385 $$x^n y'(x)=x^{2 n-1}-y(x)^2$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 386 $$y(x) \left (x^{n-1}+y(x)\right )+x^n y'(x)+x^2=0$$ [_Riccati] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 387 $$(1-n) x^{n-1}+x^{2 n-2}+x^n y'(x)+y(x)^2=0$$ [_Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✗ ODE 388 $$x^n y'(x)=a^2 x^{2 n-2}+b^2 y(x)^2$$ [[_homogeneous, class G], _Riccati] Solution method Riccati ODE, Generalized ODE Maple ✓Mathematica ✓ ODE 389 $$x^n y'(x)=x^{n-1} \left (a x^{2 n}-b y(x)^2+n y(x)\right )$$ [_rational, _Riccati] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 390 $$x^{2 n} y'(x)=-n x^{n-1}+x^n y(x) \left (x^{2 n} y(x)^2-3 x^n y(x)+1\right )+1$$ [_Abel] Solution method Abel ODE, First kind Maple ✓Mathematica ✓ ODE 391 $$x^k y'(x)=a x^m+b y(x)^n$$ [_Chini] Solution method Change of Variable, new dependent variable Maple ✗Mathematica ✗ ODE 392 $$\sqrt {x^2+1} y'(x)=2 x-y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 393 $$\sqrt {1-x^2} y'(x)=y(x)^2+1$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 394 $$\left (x-\sqrt {x^2+1}\right ) y'(x)=y(x)+\sqrt {y(x)^2+1}$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 395 $$\sqrt {a^2+x^2} y'(x)+y(x)+x=\sqrt {a^2+x^2}$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 396 $$\sqrt {b^2+x^2} y'(x)=\sqrt {a^2+y(x)^2}$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 397 $$\sqrt {b^2-x^2} y'(x)=\sqrt {a^2-y(x)^2}$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 398 $$x \sqrt {a^2+x^2} y'(x)=y(x) \sqrt {b^2+y(x)^2}$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 399 $$x \sqrt {x^2-a^2} y'(x)=y(x) \sqrt {y(x)^2-b^2}$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 400 $$\sqrt {X} y'(x)+\sqrt {Y}=0$$ [_quadrature] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 401 $$\sqrt {X} y'(x)=\sqrt {Y}$$ [_quadrature] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 402 $$x^{3/2} y'(x)=a+b x^{3/2} y(x)^2$$ [_rational, [_Riccati, _special]] Solution method Abel ODE, First kind Maple ✓Mathematica ✓ ODE 403 $$\sqrt {x^3+1} y'(x)=\sqrt {y(x)^3+1}$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 404 $$\sqrt {(1-x) x (1-a x)} y'(x)=\sqrt {(1-y(x)) y(x) (1-a y(x))}$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 405 $$\sqrt {1-x^4} y'(x)=\sqrt {1-y(x)^4}$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 406 $$\sqrt {x^4+x^2+1} y'(x)=\sqrt {y(x)^4+y(x)^2+1}$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 407 $$\sqrt {X} y'(x)=0$$ [_quadrature] Solution method Separable ODE, Dependent variable missing Maple ✓Mathematica ✓ ODE 408 $$\sqrt {X} y'(x)+\sqrt {Y}=0$$ [_quadrature] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 409 $$\sqrt {X} y'(x)=\sqrt {Y}$$ [_quadrature] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 410 $$\left (x^3+1\right )^{2/3} y'(x)+\left (y(x)^3+1\right )^{2/3}=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 411 $$\left (\text {a0}+\text {a1} x+4 x^3\right )^{2/3} y'(x)+\left (\text {a0}+\text {a1} y(x)+4 y(x)^3\right )^{2/3}=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 412 $$X^{2/3} y'(x)=Y^{2/3}$$ [_quadrature] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 413 $$\left (a+\cos ^2\left (\frac {x}{2}\right )\right ) y'(x)=y(x) \tan \left (\frac {x}{2}\right ) \left (a-y(x)+\cos ^2\left (\frac {x}{2}\right )+1\right )$$ [_Bernoulli] Solution method Change of Variable, Two new variables Maple ✓Mathematica ✓ ODE 414 $$\left (1-4 \cos ^2(x)\right ) y'(x)=y(x) \left (4 \cos ^2(x)+1\right ) \tan (x)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 415 $$(1-\sin (x)) y'(x)+y(x) \cos (x)=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 416 $$y'(x) (\cos (x)-\sin (x))+y(x) (\sin (x)+\cos (x))=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 417 $$y'(x) \left (\text {a0}+\text {a1} \sin ^2(x)\right )+\text {a2} x \left (\text {a1} \sin ^2(x)+\text {a3}\right )+\text {a1} y(x) \sin (2 x)=0$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 418 $$\left (x-e^x\right ) y'(x)+\left (1-e^x\right ) y(x)+e^x x=0$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 419 $$x \log (x) y'(x)=a x (\log (x)+1)-y(x)$$ [_linear] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 420 $$y(x) y'(x)+x=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 421 $$e^{x^2} x+y(x) y'(x)=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 422 $$x^3+y(x) y'(x)+y(x)=0$$ [_rational, [_Abel, 2nd type, class A]] Solution method Abel ODE, Second kind Maple ✗Mathematica ✗ ODE 423 $$a x+b y(x)+y(x) y'(x)=0$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 424 $$y(x) y'(x)+e^{-x} x (y(x)+1)=0$$ [_separable] Solution method Linear ODE Maple ✓Mathematica ✓ ODE 425 $$f(x)+y(x) y'(x)=g(x) y(x)$$ [[_Abel, 2nd type, class A]] Solution method Exact equation, integrating factor Maple ✗Mathematica ✗ ODE 426 $$y(x) y'(x)+y(x)^2+4 x (x+1)=0$$ [[_homogeneous, class D], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 427 $$y(x) y'(x)=a x+b y(x)^2$$ [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 428 $$y(x) y'(x)=a y(x)^2+b \cos (c+x)$$ [_Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 429 $$y(x) y'(x)=\text {a0}+\text {a1} y(x)+\text {a2} y(x)^2$$ [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓Mathematica ✓ ODE 430 $$y(x) y'(x)=a x+b x y(x)^2$$ [_separable] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 431 $$y(x) y'(x)=\csc ^2(x)-y(x)^2 \cot (x)$$ [_Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 432 $$y(x) y'(x)=\sqrt {a^2+y(x)^2}$$ [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓Mathematica ✓ ODE 433 $$y(x) y'(x)=\sqrt {y(x)^2-a^2}$$ [_quadrature] Solution method Separable ODE, Independent variable missing Maple ✓Mathematica ✓ ODE 434 $$g(x) f\left (x^2+y(x)^2\right )+y(x) y'(x)+x=0$$ [NONE] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 435 $$(y(x)+1) y'(x)=y(x)+x$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 436 $$(y(x)+1) y'(x)=x^2 (1-y(x))$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 437 $$(y(x)+x) y'(x)+y(x)=0$$ [[_homogeneous, class A], _exact, _rational, [_Abel, 2nd type, class A]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 438 $$(x-y(x)) y'(x)=y(x)$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 439 $$(y(x)+x) y'(x)-y(x)+x=0$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 440 $$(y(x)+x) y'(x)=x-y(x)$$ [[_homogeneous, class A], _exact, _rational, [_Abel, 2nd type, class A]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 441 $$1-y'(x)=y(x)+x$$ [[_linear, class A]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 442 $$(x-y(x)) y'(x)=y(x) (2 x y(x)+1)$$ [[_homogeneous, class D], _rational, [_Abel, 2nd type, class A]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 443 $$(y(x)+x) y'(x)+\tan (y(x))=0$$ [[_1st_order, _with_symmetry_[F(x)*G(y),0]]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 444 $$(x-y(x)) y'(x)=\left (e^{-\frac {x}{y(x)}}+1\right ) y(x)$$ [[_homogeneous, class A], _dAlembert] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 445 $$(y(x)+x+1) y'(x)+3 y(x)+4 x+1=0$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 446 $$(y(x)+x+2) y'(x)=-y(x)-x+1$$ [[_homogeneous, class C], _exact, _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 447 $$(-y(x)-x+3) y'(x)=-3 y(x)+x+1$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 448 $$(y(x)-x+3) y'(x)=3 y(x)-4 x+11$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 449 $$(y(x)+2 x) y'(x)-2 y(x)+x=0$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 450 $$(-y(x)+2 x+2) y'(x)+3 (-y(x)+2 x+1)=0$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 451 $$(-y(x)+2 x+3) y'(x)+2=0$$ [[_homogeneous, class C], [_Abel, 2nd type, class C], _dAlembert] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 452 $$(-y(x)+2 x+4) y'(x)-2 y(x)+x+5=0$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 453 $$(-y(x)-2 x+5) y'(x)-2 y(x)-x+4=0$$ [[_homogeneous, class C], _exact, _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 454 $$(y(x)-3 x+1) y'(x)=2 (x-y(x))$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 455 $$(y(x)-3 x+2) y'(x)-3 y(x)-2 x+5=0$$ [[_homogeneous, class C], _exact, _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 456 $$(4 x-y(x)) y'(x)-5 y(x)+2 x=0$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 457 $$(-y(x)-4 x+6) y'(x)=2 x-y(x)$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 458 $$(-y(x)+5 x+1) y'(x)-5 y(x)+x+5=0$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 459 $$y'(x) (a+b x+y(x))+a-b x-y(x)=0$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 460 $$\left (x^2-y(x)\right ) y'(x)+x=0$$ [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]], [_Abel, 2nd type, class C]] Solution method Change of Variable, new independent variable Maple ✓Mathematica ✓ ODE 461 $$\left (x^2-y(x)\right ) y'(x)=4 x y(x)$$ [[_homogeneous, class G], _rational, [_Abel, 2nd type, class A]] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 462 $$y'(x) (y(x)-\cot (x) \csc (x))+y(x) \csc (x) (y(x) \cos (x)+1)=0$$ [[_Abel, 2nd type, class A]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 463 $$x^2+2 y(x) y'(x)+y(x)^2+2 x=0$$ [[_homogeneous, class D], _rational, _Bernoulli] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 464 $$2 y(x) y'(x)=x^3+x y(x)^2$$ [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 465 $$(x-2 y(x)) y'(x)=y(x)$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 466 $$(2 y(x)+x) y'(x)-y(x)+2 x=0$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 467 $$(x-2 y(x)) y'(x)+y(x)+2 x=0$$ [[_homogeneous, class A], _exact, _rational, [_Abel, 2nd type, class A]] Solution method Exact equation Maple ✓Mathematica ✓ ODE 468 $$(-2 y(x)+x+1) y'(x)=-y(x)+2 x+1$$ [[_homogeneous, class C], _exact, _rational, [_Abel, 2nd type, class A]] Solution method Exact equation Maple ✓Mathematica ✓ ODE 469 $$(2 y(x)+x+1) y'(x)-2 y(x)-x+1=0$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 470 $$(2 y(x)+x+1) y'(x)-4 y(x)+x+7=0$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 471 $$x^2+2 (y(x)+x) y'(x)+2 y(x)=0$$ [_exact, _rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class A]] Solution method Exact equation Maple ✓Mathematica ✓ ODE 472 $$(-2 y(x)+2 x+3) y'(x)=-2 y(x)+6 x+1$$ [[_homogeneous, class C], _exact, _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 473 $$(-2 y(x)-4 x+1) y'(x)+y(x)+2 x=0$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 474 $$(6 x-2 y(x)) y'(x)=-y(x)+3 x+2$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 475 $$(2 y(x)+9 x+19) y'(x)-6 y(x)-2 x+18=0$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 476 $$\left (x^3+2 y(x)\right ) y'(x)=3 x (2-x y(x))$$ [_exact, _rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class A]] Solution method Exact equation Maple ✓Mathematica ✓ ODE 477 $$y'(x) (\tan (x) \sec (x)-2 y(x))+\sec (x) (2 y(x) \sin (x)+1)=0$$ [[_Abel, 2nd type, class A]] Solution method Exact equation, integrating factor Maple ✗Mathematica ✗ ODE 478 $$\left (e^{-x} x-2 y(x)\right ) y'(x)=2 e^{-2 x} x-\left (-2 y(x)+e^{-x} x+e^{-x}\right ) y(x)$$ [[_Abel, 2nd type, class B]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 479 $$3 y(x) y'(x)+5 \cot (x) \cos ^2(y(x)) \cot (y(x))=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 480 $$3 (2-y(x)) y'(x)+x y(x)=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 481 $$(x-3 y(x)) y'(x)-y(x)+3 x+4=0$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 482 $$(-3 y(x)-x+4) y'(x)-3 y(x)-x+3=0$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 483 $$(3 y(x)+2 x+2) y'(x)=-3 y(x)-2 x+1$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 484 $$(-3 y(x)-2 x+5) y'(x)-3 y(x)-2 x+1=0$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 485 $$(-3 y(x)+9 x+1) y'(x)-y(x)+3 x+2=0$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 486 $$(4 y(x)+x) y'(x)-y(x)+4 x=0$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 487 $$(4 y(x)+2 x+3) y'(x)=2 y(x)+x+1$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 488 $$(-4 y(x)+2 x+5) y'(x)=-2 y(x)+x+3$$ [[_homogeneous, class C], _exact, _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 489 $$(-4 y(x)+3 x+5) y'(x)=-3 y(x)+7 x+2$$ [[_homogeneous, class C], _exact, _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 490 $$4 (-y(x)-x+1) y'(x)-x+2=0$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class C], _dAlembert] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 491 $$(-4 y(x)-11 x+11) y'(x)=-25 y(x)-8 x+62$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 492 $$(5 y(x)+3 x+6) y'(x)=7 y(x)+x+2$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 493 $$(5 y(x)+7 x) y'(x)+8 y(x)+10 x=0$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 494 $$\left (4 x^3+5 y(x)+x\right ) y'(x)+7 x^3+3 x^2 y(x)+4 y(x)=0$$ [_rational, [_Abel, 2nd type, class A]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 495 $$(6 y(x)-x+5) y'(x)=4 y(x)-x+3$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 496 $$3 (2 y(x)+x) y'(x)=-2 y(x)-x+1$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 497 $$(7 y(x)-3 x+3) y'(x)+3 y(x)-7 x+7=0$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 498 $$(9 y(x)+x+1) y'(x)+5 y(x)+x+1=0$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 499 $$(-12 y(x)+5 x+8) y'(x)=-5 y(x)+2 x+3$$ [[_homogeneous, class C], _exact, _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 500 $$(-16 y(x)+7 x+140) y'(x)+y(x)+8 x+25=0$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 501 $$(21 y(x)+9 x+3) y'(x)=-5 y(x)+7 x+45$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 502 $$y'(x) (a x+b y(x))+x=0$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class C], _dAlembert] Solution method Change of Variable, new independent variable Maple ✓Mathematica ✓ ODE 503 $$y'(x) (a x+b y(x))+y(x)=0$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]] Solution method Change of Variable, new independent variable Maple ✓Mathematica ✓ ODE 504 $$y'(x) (a x+b y(x))+a y(x)+b x=0$$ [[_homogeneous, class A], _exact, _rational, [_Abel, 2nd type, class A]] Solution method Exact equation Maple ✓Mathematica ✓ ODE 505 $$y'(x) (a x+b y(x))=a y(x)+b x$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 506 $$\text {a1}+y'(x) (\text {a2}+b x+\text {c2} y(x))+b y(x)+\text {b1} x=0$$ [[_homogeneous, class C], _exact, _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 507 $$y'(x) (\text {a2}+\text {b2} y(x)+\text {c2} y(x))=\text {a1}+\text {b1} x+\text {c1} y(x)$$ [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 508 $$x y(x) y'(x)+y(x)^2+1=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 509 $$x y(x) y'(x)=y(x)^2+x$$ [[_homogeneous, class D], _rational, _Bernoulli] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 510 $$x^2+x y(x) y'(x)+y(x)^2=0$$ [[_homogeneous, class A], _rational, _Bernoulli] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 511 $$x^4+x y(x) y'(x)-y(x)^2=0$$ [[_homogeneous, class D], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 512 $$x y(x) y'(x)=a x^3 \cos (x)+y(x)^2$$ [[_homogeneous, class D], _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 513 $$x y(x) y'(x)=x^2-x y(x)+y(x)^2$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 514 $$2 x^2+x y(x) y'(x)-2 x y(x)-y(x)^2=0$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 515 $$x y(x) y'(x)=a+b y(x)^2$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 516 $$x y(x) y'(x)=a x^n+b y(x)^2$$ [[_homogeneous, class G], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 517 $$x y(x) y'(x)=\left (x^2+1\right ) \left (1-y(x)^2\right )$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 518 $$x^2 \cot ^{-1}\left (\frac {y(x)}{x}\right )+x y(x) y'(x)-y(x)^2=0$$ [[_homogeneous, class A], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 519 $$x^2 e^{-\frac {2 y(x)}{x}}+x y(x) y'(x)-y(x)^2=0$$ [[_homogeneous, class A], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 520 $$(x y(x)+1) y'(x)+y(x)^2=0$$ [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 521 $$x (y(x)+1) y'(x)-(1-x) y(x)=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 522 $$x (1-y(x)) y'(x)+(x+1) y(x)=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 523 $$x (1-y(x)) y'(x)+(1-x) y(x)=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 524 $$a x+x (y(x)+2) y'(x)=0$$ [_quadrature] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 525 $$(x (-y(x))+3 x+2) y'(x)+y(x)=0$$ [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]], [_Abel, 2nd type, class B]] Solution method Change of Variable, new independent variable Maple ✓Mathematica ✓ ODE 526 $$x (y(x)+4) y'(x)=y(x)^2+2 y(x)+2 x$$ [_rational, [_Abel, 2nd type, class B]] Solution method Homogeneous equation, special Maple ✓Mathematica ✓ ODE 527 $$x (a+y(x)) y'(x)+b x+c y(x)=0$$ [_rational, [_Abel, 2nd type, class B]] Solution method Change of Variable, new independent variable Maple ✗Mathematica ✗ ODE 528 $$x (a+y(x)) y'(x)=y(x) (A+B x)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 529 $$x (y(x)+x) y'(x)+y(x)^2=0$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 530 $$x (x-y(x)) y'(x)+y(x)^2=0$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 531 $$x (y(x)+x) y'(x)=x^2+y(x)^2$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 532 $$2 x^2+x (x-y(x)) y'(x)+3 x y(x)-y(x)^2=0$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 533 $$x \sqrt {x^2-y(x)^2}+x (y(x)+x) y'(x)-y(x) (y(x)+x)=0$$ [[_homogeneous, class A], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 534 $$(a+x (y(x)+x)) y'(x)=b y(x) (y(x)+x)$$ [_rational, [_Abel, 2nd type, class B]] Solution method Homogeneous equation, special Maple ✗Mathematica ✗ ODE 535 $$x (y(x)+2 x) y'(x)=x^2+x y(x)-y(x)^2$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 536 $$4 x^2+x (4 x-y(x)) y'(x)-6 x y(x)-y(x)^2=0$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 537 $$x \left (x^3+y(x)\right ) y'(x)=\left (x^3-y(x)\right ) y(x)$$ [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 538 $$x \left (2 x^3+y(x)\right ) y'(x)=\left (2 x^3-y(x)\right ) y(x)$$ [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 539 $$x \left (2 x^3+y(x)\right ) y'(x)=6 y(x)^2$$ [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]] Solution method Change of Variable, new independent variable Maple ✓Mathematica ✓ ODE 540 $$(1-x) y(x) y'(x)+x (1-y(x))=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 541 $$(a+x) (b+x) y'(x)=x y(x)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 542 $$-2 x^3+2 x y(x) y'(x)-y(x)^2+1=0$$ [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 543 $$a+2 x y(x) y'(x)+y(x)^2=0$$ [_separable] Solution method Exact equation Maple ✓Mathematica ✓ ODE 544 $$2 x y(x) y'(x)=a x+y(x)^2$$ [[_homogeneous, class G], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 545 $$x^2+2 x y(x) y'(x)+y(x)^2=0$$ [[_homogeneous, class A], _exact, _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 546 $$2 x y(x) y'(x)=x^2+y(x)^2$$ [[_homogeneous, class A], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 547 $$2 x y(x) y'(x)=4 (2 x+1) x^2+y(x)^2$$ [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 548 $$x^2 \left (a x^3+1\right )+2 x y(x) y'(x)=6 y(x)^2$$ [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 549 $$3 x^2+(2 x y(x)-x+3) y'(x)+y(x)^2-y(x)=0$$ [_exact, _rational, [_Abel, 2nd type, class B]] Solution method Exact equation Maple ✓Mathematica ✓ ODE 550 $$x (x-2 y(x)) y'(x)+y(x)^2=0$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 551 $$x (2 y(x)+x) y'(x)+(2 x-y(x)) y(x)=0$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 552 $$x (x-2 y(x)) y'(x)+(2 x-y(x)) y(x)=0$$ [[_homogeneous, class A], _exact, _rational, [_Abel, 2nd type, class B]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 553 $$x (-2 y(x)+x+1) y'(x)+y(x) (y(x)-2 x+1)=0$$ [_rational, [_Abel, 2nd type, class B]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 554 $$x (-2 y(x)-x+1) y'(x)+y(x) (y(x)+2 x+1)=0$$ [_rational, [_Abel, 2nd type, class B]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 555 $$2 x \left (2 x^2+y(x)\right ) y'(x)+y(x) \left (12 x^2+y(x)\right )=0$$ [[_homogeneous, class G], _exact, _rational, [_Abel, 2nd type, class B]] Solution method Exact equation Maple ✓Mathematica ✓ ODE 556 $$-3 x^2+2 (x+1) y(x) y'(x)+y(x)^2+2 x=0$$ [_exact, _rational, _Bernoulli] Solution method Exact equation Maple ✓Mathematica ✓ ODE 557 $$x (3 y(x)+2 x) y'(x)=y(x)^2$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 558 $$x (3 y(x)+2 x) y'(x)+3 (y(x)+x)^2=0$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 559 $$\left (x^2+6 x y(x)+3\right ) y'(x)+3 y(x)^2+2 x y(x)+2 x=0$$ [_exact, _rational, [_Abel, 2nd type, class B]] Solution method Exact equation Maple ✓Mathematica ✓ ODE 560 $$x^3+3 x (2 y(x)+x) y'(x)+3 y(x) (y(x)+2 x)=0$$ [_exact, _rational, [_Abel, 2nd type, class B]] Solution method Exact equation Maple ✓Mathematica ✓ ODE 561 $$a x y(x) y'(x)=x^2+y(x)^2$$ [[_homogeneous, class A], _rational, _Bernoulli] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 562 $$a x y(x) y'(x)+x^2-y(x)^2=0$$ [[_homogeneous, class A], _rational, _Bernoulli] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 563 $$x y'(x) (a+b y(x))=c y(x)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 564 $$x (x-a y(x)) y'(x)=y(x) (y(x)-a x)$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 565 $$y'(x) (x (A x+B y(x))+\text {a0}+\text {a1} x+\text {a2} y(x))=y(x) (A x+B y(x))+\text {b0}+\text {b1} x+\text {b2} y(x)$$ [_rational, [_Abel, 2nd type, class B]] Solution method Homogeneous equation, Jacobi equation Maple ✓Mathematica ✗ ODE 566 $$y'(x) (x (\text {a1}+\text {b2} x+\text {c2} y(x))+\text {a1}+\text {b1} x+\text {c1} y(x))=y(x) (\text {a2}+\text {b2} x+\text {c2} y(x))+\text {a3}+\text {b3} x+\text {c2} y(x)$$ [_rational, [_Abel, 2nd type, class B]] Solution method Homogeneous equation, Jacobi equation Maple ✓Mathematica ✗ ODE 567 $$x y'(x) \left (a y(x)+x^n\right )+y(x)^2 (b+c y(x))=0$$ [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]], [_Abel, 2nd type, class C]] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 568 $$\left (1-x^2 y(x)\right ) y'(x)-x y(x)^2+1=0$$ [_exact, _rational, [_Abel, 2nd type, class B]] Solution method Exact equation Maple ✓Mathematica ✓ ODE 569 $$\left (1-x^2 y(x)\right ) y'(x)+x y(x)^2-1=0$$ [_rational, [_Abel, 2nd type, class B]] Solution method Homogeneous equation, special Maple ✓Mathematica ✓ ODE 570 $$x (1-x y(x)) y'(x)+y(x) (x y(x)+1)=0$$ [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 571 $$x (x y(x)+2) y'(x)=2 x^3-x y(x)^2-2 y(x)+3$$ [_exact, _rational, [_Abel, 2nd type, class B]] Solution method Exact equation Maple ✓Mathematica ✓ ODE 572 $$x (2-x y(x)) y'(x)-x (x y(x)+1) y(x)^2+2 y(x)=0$$ [[_homogeneous, class G], _rational, [_Abel, 2nd type, class C]] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 573 $$x (3-x y(x)) y'(x)=y(x) (x y(x)-1)$$ [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 574 $$x^2 (1-y(x)) y'(x)+(1-x) y(x)=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 575 $$x^2 (1-y(x)) y'(x)+(x+1) y(x)^2=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 576 $$\left (x^2+1\right ) y(x) y'(x)+x \left (1-y(x)^2\right )=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 577 $$\left (1-x^2\right ) y(x) y'(x)+2 x^2+x y(x)^2=0$$ [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 578 $$2 x^2 y(x) y'(x)=x^2 (2 x+1)-y(x)^2$$ [[_homogeneous, class D], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 579 $$x (1-2 x y(x)) y'(x)+y(x) (2 x y(x)+1)=0$$ [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]] Solution method Change of Variable, Two new variables Maple ✓Mathematica ✓ ODE 580 $$x (2 x y(x)+1) y'(x)+y(x) (3 x y(x)+2)=0$$ [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]] Solution method Homogeneous equation, isobaric equation Maple ✓Mathematica ✓ ODE 581 $$y(x) \left (-x^2 y(x)^2+2 x y(x)+1\right )+x (2 x y(x)+1) y'(x)=0$$ [[_homogeneous, class G], _rational, [_Abel, 2nd type, class C]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 582 $$x^2 (x-2 y(x)) y'(x)=2 x^3-4 x y(x)^2+y(x)^3$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class C], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 583 $$2 x (x+1) y(x) y'(x)=y(x)^2+1$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 584 $$3 x^2 y(x) y'(x)+2 x y(x)^2+1=0$$ [[_homogeneous, class G], _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 585 $$x^2 (4 x-3 y(x)) y'(x)=y(x) \left (6 x^2-3 x y(x)+2 y(x)^2\right )$$ [[_homogeneous, class A], _rational, [_Abel, 2nd type, class C], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 586 $$\left (1-x^3 y(x)\right ) y'(x)=x^2 y(x)^2$$ [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 587 $$a+2 x^3 y(x) y'(x)+3 x^2 y(x)^2=0$$ [[_homogeneous, class G], _exact, _rational, _Bernoulli] Solution method Exact equation Maple ✓Mathematica ✓ ODE 588 $$x \left (3-2 x^2 y(x)\right ) y'(x)=3 x^2 y(x)^2-3 y(x)+4 x$$ [_exact, _rational, [_Abel, 2nd type, class B]] Solution method Exact equation Maple ✓Mathematica ✓ ODE 589 $$x \left (2 x^2 y(x)+3\right ) y'(x)+y(x) \left (3 x^2 y(x)+4\right )=0$$ [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 590 $$3 x^4+8 x^3 y(x) y'(x)-6 x^2 y(x)^2-y(x)^4=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 591 $$x y(x) \left (a+b x^2\right ) y'(x)=A+B y(x)^2$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 592 $$3 x^4 y(x) y'(x)=1-2 x^3 y(x)^2$$ [[_homogeneous, class G], _rational, _Bernoulli] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 593 $$x^7 y(x) y'(x)=5 x^3 y(x)+2 \left (x^2+1\right )$$ [_rational, [_Abel, 2nd type, class B]] Solution method Abel ODE, Second kind Maple ✓Mathematica ✓ ODE 594 $$\sqrt {x^2+1} y(x) y'(x)+x \sqrt {y(x)^2+1}=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 595 $$\sqrt {x^2+1} (y(x)+1) y'(x)=y(x)^3$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 596 $$y'(x) (\text {g0}(x)+\text {g1}(x) y(x))=\text {f0}(x)+\text {f1}(x) y(x)+\text {f2}(x) y(x)^2+\text {f3}(x) y(x)^3$$ [[_Abel, 2nd type, class C]] Solution method Abel ODE, Second kind Maple ✗Mathematica ✗ ODE 597 $$y(x)^2 y'(x)+x (2-y(x))=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 598 $$y(x)^2 y'(x)=x \left (y(x)^2+1\right )$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 599 $$\left (y(x)^2+x\right ) y'(x)+y(x)=a+b x$$ [_exact, _rational] Solution method Exact equation Maple ✓Mathematica ✓ ODE 600 $$\left (x-y(x)^2\right ) y'(x)=x^2-y(x)$$ [_exact, _rational] Solution method Exact equation Maple ✓Mathematica ✓ ODE 601 $$\left (x^2+y(x)^2\right ) y'(x)+x y(x)=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 602 $$\left (x^2+y(x)^2\right ) y'(x)=x y(x)$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 603 $$\left (x^2-y(x)^2\right ) y'(x)=2 x y(x)$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 604 $$\left (x^2-y(x)^2\right ) y'(x)+x (2 y(x)+x)=0$$ [[_homogeneous, class A], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓Mathematica ✓ ODE 605 $$\left (x^2+y(x)^2\right ) y'(x)+2 x (y(x)+2 x)=0$$ [[_homogeneous, class A], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓Mathematica ✓ ODE 606 $$\left (-x^2+y(x)^2+1\right ) y'(x)=x^2-y(x)^2+1$$ [[_1st_order, _with_linear_symmetries], _rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 607 $$\left (a^2+x^2+y(x)^2\right ) y'(x)+2 x y(x)=0$$ [_exact, _rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]] Solution method Exact equation Maple ✓Mathematica ✓ ODE 608 $$\left (a^2+x^2+y(x)^2\right ) y'(x)+b^2+x^2+2 x y(x)=0$$ [_exact, _rational] Solution method Exact equation Maple ✓Mathematica ✓ ODE 609 $$\left (x^2+y(x)^2+x\right ) y'(x)=y(x)$$ [_rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 610 $$\left (3 x^2-y(x)^2\right ) y'(x)=2 x y(x)$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 611 $$\left (x^4+y(x)^2\right ) y'(x)=4 x^3 y(x)$$ [[_homogeneous, class G], _rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 612 $$y(x) (y(x)+1) y'(x)=x (x+1)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 613 $$\left (y(x)^2+2 y(x)+x\right ) y'(x)+y(x)^2 (y(x)+x)^2+y(x) (y(x)+1)=0$$ [_rational] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 614 $$\left (x^2+y(x)^2+2 y(x)\right ) y'(x)+2 x=0$$ [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 615 $$\left (x^3-y(x)^2+2 y(x)\right ) y'(x)+3 x^2 y(x)=0$$ [_exact, _rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]] Solution method Exact equation Maple ✓Mathematica ✓ ODE 616 $$\left (y(x)^2+x y(x)+y(x)+1\right ) y'(x)+y(x)+1=0$$ [[_1st_order, _with_linear_symmetries], _rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 617 $$(y(x)+x)^2 y'(x)=a^2$$ [[_homogeneous, class C], _dAlembert] Solution method Equation linear in the variables, $$y'(x)=f(a+b x+ c y(x))$$ Maple ✓Mathematica ✓ ODE 618 $$(x-y(x))^2 y'(x)=a^2$$ [[_homogeneous, class C], _dAlembert] Solution method Equation linear in the variables, $$y'(x)=f(a+b x+ c y(x))$$ Maple ✓Mathematica ✓ ODE 619 $$\left (x^2+2 x y(x)-y(x)^2\right ) y'(x)+x^2-2 x y(x)+y(x)^2=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 620 $$(x-y(x))^2 y'(x)=(-y(x)+x+1)^2$$ [[_homogeneous, class C], _rational, _dAlembert] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 621 $$(y(x)+x)^2 y'(x)=(y(x)+x+2)^2$$ [[_homogeneous, class C], _rational, _dAlembert] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 622 $$(y(x)+x)^2 y'(x)=x^2-2 x y(x)+5 y(x)^2$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 623 $$y'(x) (a+b+y(x)+x)^2=2 (a+y(x))^2$$ [[_homogeneous, class C], _rational] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 624 $$\left (2 x^2+4 x y(x)-y(x)^2\right ) y'(x)=x^2-4 x y(x)-2 y(x)^2$$ [[_homogeneous, class A], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓Mathematica ✓ ODE 625 $$(y(x)+3 x)^2 y'(x)=4 y(x) (2 y(x)+3 x)$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 626 $$(-y(x)-3 x+1)^2 y'(x)=(-4 y(x)-6 x+3) (1-2 y(x))$$ [[_homogeneous, class C], _rational] Solution method Change of Variable, Two new variables Maple ✓Mathematica ✓ ODE 627 $$y'(x) \left (\cot (x)-2 y(x)^2\right )=y(x)^3 \csc (x) \sec (x)$$ [y=_G(x,y')] Solution method Change of Variable, new independent variable Maple ✗Mathematica ✓ ODE 628 $$3 y(x)^2 y'(x)=a y(x)^3+x+1$$ [_rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 629 $$\left (x^2-3 y(x)^2\right ) y'(x)+2 x y(x)+1=0$$ [_exact, _rational] Solution method Exact equation Maple ✓Mathematica ✓ ODE 630 $$\left (2 x^2+3 y(x)^2\right ) y'(x)+x (y(x)+3 x)=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Exact equation Maple ✓Mathematica ✓ ODE 631 $$3 \left (x^2-y(x)^2\right ) y'(x)-2 y(x)^3+6 x (x+1) y(x)+3 e^x=0$$ [y=_G(x,y')] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 632 $$\left (3 x^2+2 x y(x)+4 y(x)^2\right ) y'(x)+2 x^2+6 x y(x)+y(x)^2=0$$ [[_homogeneous, class A], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓Mathematica ✓ ODE 633 $$(2 y(x)-3 x+1)^2 y'(x)=(-3 y(x)+2 x+4)^2$$ [[_homogeneous, class C], _rational] Solution method Equation linear in the variables, $$y'(x)=f\left (\frac {X_1}{X_2} \right )$$ Maple ✓Mathematica ✓ ODE 634 $$\left (-3 x^2 y(x)+6 y(x)^2+1\right ) y'(x)+x^2-3 x y(x)^2=0$$ [_exact, _rational] Solution method Exact equation Maple ✓Mathematica ✓ ODE 635 $$a+(x-6 y(x))^2 y'(x)-6 y(x)^2+2 x y(x)=0$$ [_exact, _rational, [_1st_order, _with_symmetry_[F(x),G(x)]]] Solution method Exact equation Maple ✓Mathematica ✓ ODE 636 $$\left (a y(x)^2+x^2\right ) y'(x)=x y(x)$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 637 $$\left (a y(x)^2+x^2+x y(x)\right ) y'(x)=a x^2+x y(x)+y(x)^2$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 638 $$\left (a x^2-a y(x)^2+2 x y(x)\right ) y'(x)-2 a x y(x)+x^2-y(x)^2=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 639 $$y'(x) \left (x^2 (a+2 b)+2 x (2 b+c) y(x)+3 c y(x)^2\right )+2 x (a+2 b) y(x)+3 a x^2+(2 b+c) y(x)^2=0$$ [[_homogeneous, class A], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓Mathematica ✓ ODE 640 $$y'(x) \left (a x^2+2 b x y(x)+c y(x)^2\right )+2 a x y(x)+b y(x)^2+k x^2=0$$ [[_homogeneous, class A], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓Mathematica ✓ ODE 641 $$x \left (1-y(x)^2\right ) y'(x)=\left (x^2+1\right ) y(x)$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 642 $$x \left (3 x-y(x)^2\right ) y'(x)+y(x) \left (5 x-2 y(x)^2\right )=0$$ [[_homogeneous, class G], _rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 643 $$x \left (x^2+y(x)^2\right ) y'(x)=y(x) \left (x^4+x^2+y(x)^2\right )$$ [[_homogeneous, class D], _rational] Solution method Homogeneous equation, $$xy'(x)=x f(x) g(u)+y(x)$$ Maple ✓Mathematica ✓ ODE 644 $$x \left (-x^2+y(x)^2+1\right ) y'(x)+y(x) \left (x^2-y(x)^2+1\right )=0$$ [_rational, [_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] Solution method Homogeneous equation, special Maple ✓Mathematica ✓ ODE 645 $$x \left (a-x^2-y(x)^2\right ) y'(x)+y(x) \left (a+x^2+y(x)^2\right )=0$$ [_rational, [_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] Solution method Homogeneous equation, special Maple ✓Mathematica ✓ ODE 646 $$x \left (2 x^2+y(x)^2\right ) y'(x)=y(x) \left (2 x^2+3 y(x)^2\right )$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 647 $$\left (x \left (a-x^2-y(x)^2\right )+y(x)\right ) y'(x)-y(x) \left (a-x^2-y(x)^2\right )+x=0$$ [[_1st_order, _with_linear_symmetries], _rational] Solution method Change of Variable, Two new variables Maple ✓Mathematica ✓ ODE 648 $$x (a+y(x))^2 y'(x)=b y(x)^2$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 649 $$x \left (x^2-x y(x)+y(x)^2\right ) y'(x)+y(x) \left (x^2+x y(x)+y(x)^2\right )=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 650 $$x \left (x^2-x y(x)-y(x)^2\right ) y'(x)=y(x) \left (x^2+x y(x)-y(x)^2\right )$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 651 $$x \left (a x y(x)+x^2+y(x)^2\right ) y'(x)=y(x) \left (b x y(x)+x^2+y(x)^2\right )$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 652 $$x \left (x^2-2 y(x)^2\right ) y'(x)=y(x) \left (2 x^2-y(x)^2\right )$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 653 $$x \left (x^2+2 y(x)^2\right ) y'(x)=y(x) \left (2 x^2+3 y(x)^2\right )$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 654 $$2 x \left (5 x^2+y(x)^2\right ) y'(x)=x^2 y(x)-y(x)^3$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 655 $$x \left (a x y(x)+x^2+2 y(x)^2\right ) y'(x)=y(x)^2 (a x+2 y(x))$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 656 $$3 x y(x)^2 y'(x)=2 x-y(x)^3$$ [[_homogeneous, class G], _exact, _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 657 $$\left (3 x y(x)^2-4 x+1\right ) y'(x)=y(x) \left (2-y(x)^2\right )$$ [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 658 $$x \left (x-3 y(x)^2\right ) y'(x)+y(x) \left (2 x-y(x)^2\right )=0$$ [[_homogeneous, class G], _exact, _rational] Solution method Exact equation Maple ✓Mathematica ✓ ODE 659 $$x^3+3 x \left (y(x)^2+x\right ) y'(x)-3 x y(x)-2 y(x)^3=0$$ [_rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 660 $$x \left (-3 x^3 y(x)+x^3+4 y(x)^2\right ) y'(x)=6 y(x)^3$$ [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]] Solution method Change of Variable, new independent variable Maple ✓Mathematica ✓ ODE 661 $$6 x y(x)^2 y'(x)+2 y(x)^3+x=0$$ [[_homogeneous, class G], _exact, _rational, _Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 662 $$x \left (6 y(x)^2+x\right ) y'(x)-3 y(x)^3+x y(x)=0$$ [[_homogeneous, class G], _rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 663 $$x \left (x^2-6 y(x)^2\right ) y'(x)=4 y(x) \left (x^2+3 y(x)^2\right )$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 664 $$x \left (3 x-7 y(x)^2\right ) y'(x)+y(x) \left (5 x-3 y(x)^2\right )=0$$ [[_homogeneous, class G], _rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 665 $$x^3+x^2 y(x)^2 y'(x)-x+1=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 666 $$\left (1-x^2 y(x)^2\right ) y'(x)=x y(x)^3$$ [[_homogeneous, class G], _rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 667 $$\left (1-x^2 y(x)^2\right ) y'(x)=y(x)^2 (x y(x)+1)$$ [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 668 $$x \left (x y(x)^2+1\right ) y'(x)+y(x)=0$$ [[_homogeneous, class G], _rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 669 $$x \left (x y(x)^2+1\right ) y'(x)=y(x) \left (2-3 x y(x)^2\right )$$ [[_homogeneous, class G], _rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 670 $$x^2 (a+y(x))^2 y'(x)=\left (x^2+1\right ) \left (a^2+y(x)^2\right )$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 671 $$\left (x^2+1\right ) \left (y(x)^2+1\right ) y'(x)+2 x y(x) \left (1-y(x)^2\right )=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 672 $$\left (x^2+1\right ) \left (y(x)^2+1\right ) y'(x)+2 x y(x) (1-y(x))^2=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 673 $$\left (-x^3+6 x^2 y(x)^2+1\right ) y'(x)=x \left (-4 y(x)^3+3 x y(x)+6\right )$$ [_exact, _rational] Solution method Exact equation Maple ✓Mathematica ✓ ODE 674 $$x \left (4 x^2 y(x)-12 x y(x)^2+5 x+3\right ) y'(x)+y(x) \left (6 x^2 y(x)-8 x y(x)^2+10 x+3\right )=0$$ [_exact, _rational] Solution method Exact equation Maple ✓Mathematica ✓ ODE 675 $$x^3 \left (y(x)^2+1\right ) y'(x)+3 x^2 y(x)=0$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 676 $$y(x) \left (x^2 y(x)^2+1\right )+x (1-x y(x))^2 y'(x)=0$$ [[_homogeneous, class G], _rational] Solution method Homogeneous equation, isobaric equation Maple ✓Mathematica ✓ ODE 677 $$\left (1-x^4 y(x)^2\right ) y'(x)=x^3 y(x)^3$$ [[_homogeneous, class G], _rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 678 $$\left (3 x-y(x)^3\right ) y'(x)=x^2-3 y(x)$$ [_exact, _rational] Solution method Exact equation Maple ✓Mathematica ✓ ODE 679 $$\left (x^3-y(x)^3\right ) y'(x)+x^2 y(x)=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 680 $$x^2 (a x+3 y(x))+\left (x^3+y(x)^3\right ) y'(x)=0$$ [[_homogeneous, class A], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓Mathematica ✓ ODE 681 $$\left (-x^2 y(x)-y(x)^3+x\right ) y'(x)=x^3+x y(x)^2-y(x)$$ [_exact, _rational] Solution method Exact equation Maple ✓Mathematica ✓ ODE 682 $$\left (a^2 x+y(x) \left (x^2-y(x)^2\right )\right ) y'(x)+x \left (x^2-y(x)^2\right )=a^2 y(x)$$ [_rational] Solution method Change of Variable, Two new variables Maple ✗Mathematica ✓ ODE 683 $$y(x) \left (a+x^2+y(x)^2\right ) y'(x)=x \left (a-x^2-y(x)^2\right )$$ [_exact, _rational] Solution method Exact equation Maple ✓Mathematica ✓ ODE 684 $$y(x) \left (3 x^2+y(x)^2\right ) y'(x)+x \left (x^2+3 y(x)^2\right )=0$$ [[_homogeneous, class A], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓Mathematica ✓ ODE 685 $$y(x) \left (a-3 x^2-y(x)^2\right ) y'(x)+x \left (a-x^2+y(x)^2\right )=0$$ [_rational] Solution method Change of Variable, Two new variables Maple ✓Mathematica ✓ ODE 686 $$2 y(x)^3 y'(x)=x^3-x y(x)^2$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 687 $$y(x) \left (2 y(x)^2+1\right ) y'(x)=x \left (2 x^2+1\right )$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 688 $$x^3+y(x) \left (3 x^2+2 y(x)^2\right ) y'(x)=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 689 $$y(x) \left (5 x^2+2 y(x)^2\right ) y'(x)+x \left (x^2+5 y(x)^2\right )=0$$ [[_homogeneous, class A], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓Mathematica ✓ ODE 690 $$2 x^3+3 x^2 y(x)+\left (-x^3+x^2+3 x y(x)^2+2 y(x)^3\right ) y'(x)-y(x)^3+y(x)^2=0$$ [_rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 691 $$4 x^3+9 x^2 y(x)+\left (3 x^3+6 x^2 y(x)-3 x y(x)^2+20 y(x)^3\right ) y'(x)+6 x y(x)^2-y(x)^3=0$$ [[_homogeneous, class A], _exact, _rational, _dAlembert] Solution method Exact equation Maple ✓Mathematica ✓ ODE 692 $$\left (a y(x)^3+x^3\right ) y'(x)=x^2 y(x)$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 693 $$y'(x) \left (a x^2-b x^3+3 c x y(x)^2+2 c y(x)^3\right )+a y(x)^2+2 b x^3+3 b x^2 y(x)-c y(x)^3=0$$ [_rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 694 $$x y(x)^3 y'(x)=\left (1-x^2\right ) \left (y(x)^2+1\right )$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 695 $$x \left (x-y(x)^3\right ) y'(x)=y(x) \left (y(x)^3+3 x\right )$$ [[_homogeneous, class G], _rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 696 $$x \left (2 x^3+y(x)^3\right ) y'(x)=y(x) \left (2 x^3-x^2 y(x)+y(x)^3\right )$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 697 $$x \left (2 x^3-y(x)^3\right ) y'(x)=y(x) \left (x^3-2 y(x)^3\right )$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 698 $$x \left (x^3+3 x^2 y(x)+y(x)^3\right ) y'(x)=y(x)^2 \left (3 x^2+y(x)^2\right )$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 699 $$x \left (x^3-2 y(x)^3\right ) y'(x)=y(x) \left (2 x^3-y(x)^3\right )$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 700 $$x \left (x^4-2 y(x)^3\right ) y'(x)+y(x) \left (2 x^4+y(x)^3\right )=0$$ [[_homogeneous, class G], _rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 701 $$x \left (2 y(x)^3+y(x)+x\right ) y'(x)=(x-y(x)) y(x)$$ [_rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 702 $$\left (-7 x y(x)^3-y(x)+5 x\right ) y'(x)-y(x)^4+5 y(x)=0$$ [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 703 $$y(x) \left (1-2 x^3 y(x)\right )+x \left (1-2 x y(x)^3\right ) y'(x)=0$$ [_rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 704 $$x \left (-2 x y(x)^3-x y(x)^2+2\right ) y'(x)+2 y(x)+1=0$$ [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]] Solution method Change of Variable, new independent variable Maple ✓Mathematica ✓ ODE 705 $$\left (-10 x^2 y(x)^3+3 y(x)^2+2\right ) y'(x)=x \left (5 y(x)^4+1\right )$$ [_exact, _rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]] Solution method Exact equation Maple ✓Mathematica ✓ ODE 706 $$x y'(x) \left (a+b x y(x)^3\right )+y(x) \left (a+c x^3 y(x)\right )=0$$ [_rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 707 $$y(x) \left (1-2 x^3 y(x)^2\right )+x \left (1-2 x^2 y(x)^3\right ) y'(x)=0$$ [_rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 708 $$x (1-x y(x)) \left (1-x^2 y(x)^2\right ) y'(x)+y(x) (x y(x)+1) \left (x^2 y(x)^2+1\right )=0$$ [[_homogeneous, class G], _rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 709 $$\left (x^2-y(x)^4\right ) y'(x)=x y(x)$$ [[_homogeneous, class G], _rational] Solution method Change of Variable, new independent variable Maple ✓Mathematica ✓ ODE 710 $$\left (x^3-y(x)^4\right ) y'(x)=3 x^2 y(x)$$ [[_homogeneous, class G], _rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 711 $$\left (a^2 x^2+\left (x^2+y(x)^2\right )^2\right ) y'(x)=a^2 x y(x)$$ [_rational] Solution method Change of Variable, Two new variables Maple ✓Mathematica ✓ ODE 712 $$2 \left (x-y(x)^4\right ) y'(x)=y(x)$$ [[_homogeneous, class G], _rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 713 $$\left (-2 y(x)^4-x y(x)^3+4 x\right ) y'(x)=y(x) \left (y(x)^3+2\right )$$ [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 714 $$y(x) y'(x) \left ((a x+b y(x))^3+a x^3\right )+x \left ((a x+b y(x))^3+b y(x)^3\right )=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 715 $$\left (2 x^2 y(x)^3+x y(x)^4+2 y(x)+x\right ) y'(x)+y(x) \left (y(x)^4+1\right )=0$$ [_rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 716 $$2 x \left (x^3+y(x)^4\right ) y'(x)=y(x) \left (x^3+2 y(x)^4\right )$$ [[_homogeneous, class G], _rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 717 $$x \left (1-x^2 y(x)^4\right ) y'(x)+y(x)=0$$ [[_homogeneous, class G], _rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 718 $$\left (x^2-y(x)^5\right ) y'(x)=2 x y(x)$$ [[_homogeneous, class G], _rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 719 $$x \left (x^3+y(x)^5\right ) y'(x)=y(x) \left (x^3-y(x)^5\right )$$ [[_homogeneous, class G], _rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 720 $$y(x)^3 \left (3 x^5 y(x)^5-1\right )+x^3 \left (5 x^3 y(x)^7+1\right ) y'(x)=0$$ [_rational] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 721 $$y'(x) (\text {f1}(x,y(x))+x \text {f2}(x,y(x)))=y(x) \text {f2}(x,y(x))+\text {f3}(x,y(x))$$ [NONE] Solution method Homogeneous equation, Darbooux type Maple ✗Mathematica ✗ ODE 722 $$y'(x) (a (y(x)+x)+1)^n+a (y(x)+x)^n=0$$ [[_homogeneous, class C], _dAlembert] Solution method Exact equation Maple ✓Mathematica ✓ ODE 723 $$x y'(x) \left (a+x y(x)^n\right )+b y(x)=0$$ [[_homogeneous, class G], _rational] Solution method Change of Variable, new independent variable Maple ✓Mathematica ✓ ODE 724 $$f(x) y(x)^m y'(x)+g(x) y(x)^{m+1}+h(x) y(x)^n=0$$ [_Bernoulli] Solution method The Bernoulli ODE Maple ✓Mathematica ✓ ODE 725 $$\sqrt {b^2+y(x)^2} y'(x)=\sqrt {a^2+x^2}$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 726 $$\sqrt {b^2-y(x)^2} y'(x)=\sqrt {a^2-x^2}$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 727 $$\sqrt {Y} y'(x)=\sqrt {X}$$ [_quadrature] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 728 $$\left (\sqrt {y(x)+x}+1\right ) y'(x)+1=0$$ [[_homogeneous, class C], _dAlembert] Solution method Change of Variable, new dependent variable Maple ✓Mathematica ✓ ODE 729 $$\sqrt {x y(x)} y'(x)-y(x)+x=\sqrt {x y(x)}$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 730 $$\left (x-2 \sqrt {x y(x)}\right ) y'(x)=y(x)$$ [[_homogeneous, class A], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 731 $$\left (x^2+1\right )^{3/2} \left (y(x)+\sqrt {y(x)^2+1}\right ) y'(x)=y(x)^2+1$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 732 $$\left (x^2+1\right )^{3/2} \left (y(x)+\sqrt {y(x)^2+1}\right ) y'(x)=y(x)^2+1$$ [_separable] Solution method Separable ODE, Neither variable missing Maple ✓Mathematica ✓ ODE 733 $$\left (x-\sqrt {x^2+y(x)^2}\right ) y'(x)=y(x)$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 734 $$x \left (1-\sqrt {x^2-y(x)^2}\right ) y'(x)=y(x)$$ [y=_G(x,y')] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 735 $$x \left (\sqrt {x^2+y(x)^2}+x\right ) y'(x)+\sqrt {x^2+y(x)^2} y(x)=0$$ [[_homogeneous, class G], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 736 $$x y(x) \left (\sqrt {x^2-y(x)^2}+x\right ) y'(x)=x y(x)^2-\left (x^2-y(x)^2\right )^{3/2}$$ [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✗ ODE 737 $$\left (x-y(x)^2 \sqrt {y(x)^2-x^2}\right ) y'(x)=y(x) \left (x \sqrt {y(x)^2-x^2}+1\right )$$ [NONE] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 738 $$\left (x \sqrt {x^2+y(x)^2+1}-y(x) \left (x^2+y(x)^2\right )\right ) y'(x)=\sqrt {x^2+y(x)^2+1} y(x)+x \left (x^2+y(x)^2\right )$$ [[_1st_order, _with_linear_symmetries]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 739 $$y'(x) \left (x^2 \sec (x) \cos (y(x))+1\right )-y(x) \tan (x)+\sec (x) \sin (y(x))=0$$ [NONE] Solution method Exact equation, integrating factor Maple ✗Mathematica ✗ ODE 740 $$y'(x) \cos (y(x)) (\cos (y(x))-\sin (A) \sin (x))+\cos (x) (\cos (x)-\sin (A) \sin (y(x)))=0$$ [NONE] Solution method Exact equation Maple ✓Mathematica ✓ ODE 741 $$y'(x) (a \cos (a y(x)+b x)-b \sin (a x+b y(x)))-a \sin (a x+b y(x))+b \cos (a y(x)+b x)=0$$ [_exact] Solution method Exact equation Maple ✓Mathematica ✓ ODE 742 $$y'(x) (a \sin (x y(x))-\sin (y(x))+\cos (y(x)+x))+y(x) \sin (x y(x))+\cos (y(x)+x)+\cos (x)=0$$ [NONE] Solution method Exact equation Maple ✗Mathematica ✗ ODE 743 $$y'(x) (\cos (x) \sec (y(x))+x)+\tan (y(x))-y(x) \sin (x) \sec (y(x))=0$$ [NONE] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 744 $$y'(x) \left (x^2+2 y(x) \sin (x) \sec (y(x))\right )+2 x \tan (y(x))+y(x)^2 \cos (x) \sec (y(x))=0$$ [NONE] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 745 $$y'(x) \left (x^2 \sec ^2(y(x))-6 x y(x)+2\right )-3 y(x)^2+2 x \tan (y(x))=0$$ [_exact] Solution method Exact equation Maple ✓Mathematica ✓ ODE 746 $$y'(x) ((y(x)+x) \tan (y(x))+1)+1=0$$ [[_1st_order, _with_linear_symmetries]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 747 $$x y'(x) \left (x-y(x) \tan \left (\frac {y(x)}{x}\right )\right )+y(x) \left (y(x) \tan \left (\frac {y(x)}{x}\right )+x\right )=0$$ [[_homogeneous, class A], _dAlembert] Solution method Homogeneous equation Maple ✓Mathematica ✓ ODE 748 $$\left (x e^{y(x)}+e^x\right ) y'(x)+e^x y(x)+e^{y(x)}=0$$ [_exact] Solution method Exact equation Maple ✓Mathematica ✓ ODE 749 $$y'(x) (-\log (y(x))-2 x+1)+2 y(x)=0$$ [[_1st_order, _with_linear_symmetries]] Solution method Exact equation, integrating factor Maple ✓Mathematica ✓ ODE 750 $$y'(x) (x \cosh (y(x))+\sinh (x))+\sinh (y(x))+y(x) \cosh (x)=0$$ [_exact] Solution method Exact equation Maple ✓Mathematica ✓ ODE 751 $$(\sinh (x)+1) y'(x) \sinh (y(x))+\cosh (x) (\cosh (y(x))-1)=0$$ [_separable] Solution method Exact equation Maple ✓Mathematica ✓ ODE 752 $$y'(x)^2=a x^n$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 753 $$y'(x)^2=y(x)$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 754 $$y'(x)^2=x-y(x)$$ [[_homogeneous, class C], _dAlembert] Solution method No Missing Variables ODE, Solve for $$x$$ Maple ✓Mathematica ✓ ODE 755 $$y'(x)^2=x^2+y(x)$$ [[_homogeneous, class G]] Solution method Homogeneous ODE, The Isobaric equation Maple ✓Mathematica ✓ ODE 756 $$x^2+y'(x)^2=4 y(x)$$ [[_homogeneous, class G]] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 757 $$3 x^2+y'(x)^2=8 y(x)$$ [[_homogeneous, class G]] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 758 $$a x^2+b y(x)+y'(x)^2=0$$ [[_homogeneous, class G]] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✗Mathematica ✓ ODE 759 $$y'(x)^2=y(x)^2+1$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 760 $$y'(x)^2=1-y(x)^2$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 761 $$y'(x)^2=a^2-y(x)^2$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 762 $$y'(x)^2=a^2 y(x)^2$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 763 $$y'(x)^2=a+b y(x)^2$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 764 $$y'(x)^2=x^2 y(x)^2$$ [_separable] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 765 $$y'(x)^2=(y(x)-1) y(x)^2$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 766 $$y'(x)^2=(y(x)-a) (y(x)-b) (y(x)-c)$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 767 $$y'(x)^2=a^2 y(x)^n$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 768 $$y'(x)^2=a^2 y(x)^2 \left (1-\log ^2(y(x))\right )$$ [_quadrature] Solution method Change of variable Maple ✓Mathematica ✓ ODE 769 $$f(x) (y(x)-a) (y(x)-b)+y'(x)^2=0$$ [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] Solution method Binomial equation $$(y')^m + F(x) G(y)=0$$ Maple ✓Mathematica ✓ ODE 770 $$f(x) (y(x)-a)^2 (y(x)-b)+y'(x)^2=0$$ [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] Solution method Binomial equation $$(y')^m + F(x) G(y)=0$$ Maple ✓Mathematica ✓ ODE 771 $$f(x) (y(x)-a) (y(x)-b) (y(x)-c)+y'(x)^2=0$$ [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] Solution method Binomial equation $$(y')^m + F(x) G(y)=0$$ Maple ✓Mathematica ✓ ODE 772 $$f(x) (y(x)-a)^2 (y(x)-b) (y(x)-c)+y'(x)^2=0$$ [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] Solution method Binomial equation $$(y')^m + F(x) G(y)=0$$ Maple ✓Mathematica ✓ ODE 773 $$f(x) (y(x)-\text {a1}) (y(x)-\text {a2}) (y(x)-\text {a3}) (y(x)-\text {a4})+y'(x)^2=0$$ odeadvisor timed out Solution method Binomial equation $$(y')^m + F(x) G(y)=0$$ Maple ✓Mathematica ✓ ODE 774 $$y'(x)^2=f(x)^2 (y(x)-a) (y(x)-b) (y(x)-c)^2$$ [_separable] Solution method Change of variable Maple ✓Mathematica ✓ ODE 775 $$y'(x)^2=f(x)^2 (y(x)-a) (y(x)-b) (y(x)-u(x))^2$$ [y=_G(x,y')] Solution method Change of variable Maple ✗Mathematica ✗ ODE 776 $$y'(x)^2+2 y'(x)+x=0$$ [_quadrature] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 777 $$a (x-y(x))+y'(x)^2-2 y'(x)=0$$ [[_homogeneous, class C], _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 778 $$y'(x)^2-2 y'(x)-y(x)^2=0$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 779 $$y'(x)^2-5 y'(x)+6=0$$ [_quadrature] Solution method Missing Variables ODE, Both independent and dependent variable missing Maple ✓Mathematica ✓ ODE 780 $$y'(x)^2-7 y'(x)+12=0$$ [_quadrature] Solution method Missing Variables ODE, Both independent and dependent variable missing Maple ✓Mathematica ✓ ODE 781 $$a y'(x)+b+y'(x)^2=0$$ [_quadrature] Solution method Missing Variables ODE, Both independent and dependent variable missing Maple ✓Mathematica ✓ ODE 782 $$a y'(x)+b x+y'(x)^2=0$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$x$$ Maple ✓Mathematica ✓ ODE 783 $$a y'(x)+b y(x)+y'(x)^2=0$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 784 $$y'(x)^2+x y'(x)+1=0$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$x$$ Maple ✓Mathematica ✓ ODE 785 $$y'(x)^2+x y'(x)-y(x)=0$$ [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓Mathematica ✓ ODE 786 $$y'(x)^2-x y'(x)+y(x)=0$$ [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓Mathematica ✓ ODE 787 $$y'(x)^2-x y'(x)-y(x)=0$$ [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 788 $$y'(x)^2+x y'(x)-y(x)+x=0$$ [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s) Maple ✓Mathematica ✓ ODE 789 $$y'(x)^2+(1-x) y'(x)+y(x)=0$$ [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓Mathematica ✓ ODE 790 $$y'(x)^2-(x+1) y'(x)+y(x)=0$$ [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓Mathematica ✓ ODE 791 $$y'(x)^2-(2-x) y'(x)-y(x)+1=0$$ [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓Mathematica ✓ ODE 792 $$(a+x) y'(x)+y'(x)^2-y(x)=0$$ [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓Mathematica ✓ ODE 793 $$y'(x)^2-2 x y'(x)+1=0$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$x$$ Maple ✓Mathematica ✓ ODE 794 $$-3 x^2+2 x y'(x)+y'(x)^2=0$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 795 $$y'(x)^2+2 x y'(x)-y(x)=0$$ [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 796 $$y'(x)^2+2 x y'(x)-y(x)=0$$ [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method Change of variable Maple ✓Mathematica ✓ ODE 797 $$y'(x)^2-2 x y'(x)+2 y(x)=0$$ [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓Mathematica ✓ ODE 798 $$y'(x)^2-(2 x+1) y'(x)-(1-x) x=0$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 799 $$y'(x)^2+2 (1-x) y'(x)-2 (x-y(x))=0$$ [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 800 $$y'(x)^2+3 x y'(x)-y(x)=0$$ [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 801 $$y'(x)^2-4 (x+1) y'(x)+4 y(x)=0$$ [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, $$f(y-x y', y')=0$$ Maple ✓Mathematica ✓ ODE 802 $$a x y'(x)+y'(x)^2=b c x^2$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 803 $$-a x y'(x)+a y(x)+y'(x)^2=0$$ [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓Mathematica ✓ ODE 804 $$a x y'(x)+b x^2+c y(x)+y'(x)^2=0$$ [[_homogeneous, class G]] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✗Mathematica ✓ ODE 805 $$(a+b x) y'(x)+c+y'(x)^2=b y(x)$$ [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓Mathematica ✓ ODE 806 $$-2 x^2 y'(x)+2 x y'(x)+y'(x)^2=0$$ [_quadrature] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 807 $$a x^2 y'(x)+b x y(x)+y'(x)^2=0$$ [[_homogeneous, class G]] Solution method Homogeneous ODE, The Isobaric equation Maple ✓Mathematica ✓ ODE 808 $$a x^3 y'(x)-2 a x^2 y(x)+y'(x)^2=0$$ [[_1st_order, _with_linear_symmetries]] Solution method Homogeneous ODE, The Isobaric equation Maple ✓Mathematica ✓ ODE 809 $$-2 a x^3 y'(x)+4 a x^2 y(x)+y'(x)^2=0$$ [[_1st_order, _with_linear_symmetries]] Solution method Change of variable Maple ✓Mathematica ✓ ODE 810 $$4 x^5 y'(x)-12 x^4 y(x)+y'(x)^2=0$$ [[_1st_order, _with_linear_symmetries]] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 811 $$y'(x)^2-2 \cosh (x) y'(x)+1=0$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 812 $$y'(x)^2+y(x) y'(x)=x (y(x)+x)$$ [_quadrature] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 813 $$y'(x)^2-y(x) y'(x)+e^x=0$$ [[_1st_order, _with_linear_symmetries]] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 814 $$y'(x)^2+(y(x)+x) y'(x)+x y(x)=0$$ [_quadrature] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 815 $$y'(x)^2-2 y(x) y'(x)-2 x=0$$ [_dAlembert] Solution method No Missing Variables ODE, Solve for $$x$$ Maple ✓Mathematica ✓ ODE 816 $$y'(x)^2+(2 y(x)+1) y'(x)+(y(x)-1) y(x)=0$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Use new variable Maple ✓Mathematica ✓ ODE 817 $$y'(x)^2-2 (x-y(x)) y'(x)-4 x y(x)=0$$ [_quadrature] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 818 $$y'(x)^2-(4 y(x)+1) y'(x)+y(x) (4 y(x)+1)=0$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 819 $$y'(x)^2-2 (1-3 y(x)) y'(x)-(4-9 y(x)) y(x)=0$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 820 $$y(x) (3 a+b+9 y(x))+(a+6 y(x)) y'(x)+y'(x)^2=0$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 821 $$a y(x) y'(x)-a x+y'(x)^2=0$$ [_dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s) Maple ✓Mathematica ✓ ODE 822 $$-a y(x) y'(x)-a x+y'(x)^2=0$$ [_dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s) Maple ✓Mathematica ✓ ODE 823 $$y'(x) (a x+b y(x))+a b x y(x)+y'(x)^2=0$$ [_quadrature] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 824 $$y(x)^2 \log (a y(x))-x y(x) y'(x)+y'(x)^2=0$$ [[_1st_order, _with_symmetry_[F(x),G(y)]]] Solution method No Missing Variables ODE, Solve for $$x$$ Maple ✓Mathematica ✓ ODE 825 $$y'(x)^2-(2 x y(x)+1) y'(x)+2 x y(x)=0$$ [_quadrature] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 826 $$y'(x)^2-\left (y(x)^2+4\right ) y'(x)+y(x)^2+4=0$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Use new variable Maple ✓Mathematica ✓ ODE 827 $$-(x-y(x)) y(x) y'(x)+y'(x)^2-x y(x)^3=0$$ [_separable] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 828 $$x y(x)^2 y'(x)+y'(x)^2+y(x)^3=0$$ [[_homogeneous, class G]] Solution method No Missing Variables ODE, Solve for $$x$$ Maple ✓Mathematica ✓ ODE 829 $$-2 x^3 y(x)^2 y'(x)-4 x^2 y(x)^3+y'(x)^2=0$$ [[_1st_order, _with_linear_symmetries]] Solution method Change of variable Maple ✓Mathematica ✓ ODE 830 $$x^4 y(x)^4-x \left (x^2+y(x)^2\right ) y(x) y'(x)+y'(x)^2=0$$ [_separable] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 831 $$2 x y(x)^3 y'(x)+y'(x)^2+y(x)^4=0$$ [[_homogeneous, class G]] Solution method No Missing Variables ODE, Solve for $$x$$ Maple ✓Mathematica ✓ ODE 832 $$y'(x)^2+2 y(x) \cot (x) y'(x)-y(x)^2=0$$ [_separable] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 833 $$y'(x)^2-3 x y(x)^{2/3} y'(x)+9 y(x)^{5/3}=0$$ [[_1st_order, _with_linear_symmetries]] Solution method Change of variable Maple ✓Mathematica ✓ ODE 834 $$y'(x)^2=e^{4 x-2 y(x)} \left (y'(x)-1\right )$$ [[_homogeneous, class C], _dAlembert] Solution method Change of variable Maple ✓Mathematica ✓ ODE 835 $$2 y'(x)^2+x y'(x)-2 y(x)=0$$ [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s) Maple ✓Mathematica ✓ ODE 836 $$2 y'(x)^2-(1-x) y'(x)-y(x)=0$$ [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓Mathematica ✓ ODE 837 $$-2 x^2 y'(x)+2 y'(x)^2+3 x y(x)=0$$ [[_homogeneous, class G]] Solution method Homogeneous ODE, The Isobaric equation Maple ✓Mathematica ✓ ODE 838 $$2 y'(x)^2+2 (6 y(x)-1) y'(x)+3 y(x) (6 y(x)-1)=0$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 839 $$3 y'(x)^2-2 x y'(x)+y(x)=0$$ [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 840 $$x^2+4 x y'(x)+3 y'(x)^2-y(x)=0$$ [[_homogeneous, class G]] Solution method Change of variable Maple ✓Mathematica ✓ ODE 841 $$4 y'(x)^2=9 x$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 842 $$4 y'(x)^2+2 x e^{-2 y(x)} y'(x)-e^{-2 y(x)}=0$$ [[_1st_order, _with_linear_symmetries]] Solution method Change of variable Maple ✓Mathematica ✓ ODE 843 $$4 y'(x)^2+2 e^{2 x-2 y(x)} y'(x)-e^{2 x-2 y(x)}=0$$ [[_homogeneous, class C], _dAlembert] Solution method Change of variable Maple ✓Mathematica ✓ ODE 844 $$5 y'(x)^2+3 x y'(x)-y(x)=0$$ [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 845 $$5 y'(x)^2+6 x y'(x)-2 y(x)=0$$ [[_1st_order, _with_linear_symmetries], _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 846 $$3 x y(x)^4 y'(x)+9 y'(x)^2+y(x)^5=0$$ [[_1st_order, _with_linear_symmetries]] Solution method No Missing Variables ODE, Solve for $$x$$ Maple ✓Mathematica ✓ ODE 847 $$x y'(x)^2=a$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 848 $$x y'(x)^2=a-x^2$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 849 $$x y'(x)^2=y(x)$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 850 $$x y'(x)^2-2 y(x)+x=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 851 $$x y'(x)^2+y'(x)=y(x)$$ [_rational, _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s) Maple ✓Mathematica ✓ ODE 852 $$x y'(x)^2+2 y'(x)-y(x)=0$$ [_rational, _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s) Maple ✓Mathematica ✓ ODE 853 $$x y'(x)^2-2 y'(x)-y(x)=0$$ [_rational, _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s) Maple ✓Mathematica ✓ ODE 854 $$x y'(x)^2+4 y'(x)-2 y(x)=0$$ [_rational, _dAlembert] Solution method No Missing Variables ODE, Solve for $$x$$ Maple ✓Mathematica ✓ ODE 855 $$x y'(x)^2+x y'(x)-y(x)=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 856 $$-\left (x^2+1\right ) y'(x)+x y'(x)^2+x=0$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 857 $$a+x y'(x)^2+y(x) y'(x)=0$$ [[_homogeneous, class G], _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s) Maple ✓Mathematica ✓ ODE 858 $$a+x y'(x)^2-y(x) y'(x)=0$$ [[_homogeneous, class G], _rational, _Clairaut] Solution method Clairaut’s equation and related types, main form Maple ✓Mathematica ✓ ODE 859 $$a x+x y'(x)^2-y(x) y'(x)=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 860 $$-x^2+x y'(x)^2+y(x) y'(x)=0$$ [[_homogeneous, class G]] Solution method Homogeneous ODE, The Isobaric equation Maple ✓Mathematica ✓ ODE 861 $$x^3+x y'(x)^2+y(x) y'(x)=0$$ [[_homogeneous, class G]] Solution method Homogeneous ODE, The Isobaric equation Maple ✓Mathematica ✓ ODE 862 $$a y(x)+x y'(x)^2-y(x) y'(x)=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for $$x$$ Maple ✓Mathematica ✓ ODE 863 $$y(x) y'(x)+x y'(x)^2-y(x)^4=0$$ [[_homogeneous, class G]] Solution method No Missing Variables ODE, Solve for $$x$$ Maple ✓Mathematica ✓ ODE 864 $$(a-y(x)) y'(x)+b+x y'(x)^2=0$$ [[_1st_order, _with_linear_symmetries], _rational, _Clairaut] Solution method Clairaut’s equation and related types, $$f(y-x y', y')=0$$ Maple ✓Mathematica ✓ ODE 865 $$x y'(x)^2+(x-y(x)) y'(x)-y(x)+1=0$$ [[_1st_order, _with_linear_symmetries], _rational, _dAlembert] Solution method Clairaut’s equation and related types, $$f(y-x y', y')=0$$ Maple ✓Mathematica ✓ ODE 866 $$(a-y(x)+x) y'(x)+x y'(x)^2-y(x)=0$$ [[_1st_order, _with_linear_symmetries], _rational, _dAlembert] Solution method Clairaut’s equation and related types, $$f(y-x y', y')=0$$ Maple ✓Mathematica ✓ ODE 867 $$x y'(x)^2-(3 x-y(x)) y'(x)+y(x)=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s) Maple ✓Mathematica ✓ ODE 868 $$a-b y(x)+b x+x y'(x)^2-y(x)=0$$ [[_homogeneous, class C], _rational, _dAlembert] Solution method Clairaut’s equation and related types, $$f(y-x y', y')=0$$ Maple ✓Mathematica ✓ ODE 869 $$a+x y'(x)^2-2 y(x) y'(x)=0$$ [[_homogeneous, class G], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 870 $$x y'(x)^2+2 y(x) y'(x)-x=0$$ [[_homogeneous, class A], _dAlembert] Solution method Homogeneous ODE, $$x^n f\left (\frac {y}{x} , y' \right )=0$$, Solve for $$p$$ Maple ✓Mathematica ✓ ODE 871 $$a x+x y'(x)^2-2 y(x) y'(x)=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous ODE, $$x^n f\left (\frac {y}{x} , y' \right )=0$$, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 872 $$x y'(x)^2-2 y(x) y'(x)+2 y(x)+x=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Change of variable Maple ✓Mathematica ✓ ODE 873 $$9 x^2+x y'(x)^2-3 y(x) y'(x)=0$$ [[_homogeneous, class G]] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 874 $$x y'(x)^2-(3 y(x)+2 x) y'(x)+6 y(x)=0$$ [_quadrature] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 875 $$-a y(x) y'(x)+b+x y'(x)^2=0$$ [[_homogeneous, class G], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 876 $$a y(x) y'(x)+b x+x y'(x)^2=0$$ [[_homogeneous, class A], _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 877 $$x y'(x)^2-(x y(x)+1) y'(x)+y(x)=0$$ [_quadrature] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 878 $$(1-x) y(x) y'(x)+x y'(x)^2-y(x)^2=0$$ [_quadrature] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 879 $$\left (1-x^2 y(x)\right ) y'(x)+x y'(x)^2-x y(x)=0$$ [_quadrature] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 880 $$(x+1) y'(x)^2=y(x)$$ [[_homogeneous, class C], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 881 $$(x+1) y'(x)^2-(y(x)+x) y'(x)+y(x)=0$$ [[_1st_order, _with_linear_symmetries], _rational, _dAlembert] Solution method Clairaut’s equation and related types, $$f(y-x y', y')=0$$ Maple ✓Mathematica ✓ ODE 882 $$(a-x) y'(x)^2-b+y(x) y'(x)=0$$ [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, $$f(y-x y', y')=0$$ Maple ✓Mathematica ✓ ODE 883 $$(a+x) y'(x)^2+y'(x) (\text {a1}+\text {b1} x+\text {c1} y(x))+\text {a2}+\text {b2} x+\text {c2} y(x)=0$$ [_rational, _dAlembert] Solution method Change of variable Maple ✓Mathematica ✓ ODE 884 $$2 x y'(x)^2+(2 x-y(x)) y'(x)-y(x)+1=0$$ [_rational, _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s) Maple ✓Mathematica ✓ ODE 885 $$3 x y'(x)^2-6 y(x) y'(x)+2 y(x)+x=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 886 $$(3 x+1) y'(x)^2-3 (y(x)+2) y'(x)+9=0$$ [[_1st_order, _with_linear_symmetries], _Clairaut] Solution method Clairaut’s equation and related types, $$f(y-x y', y')=0$$ Maple ✓Mathematica ✓ ODE 887 $$(3 x+5) y'(x)^2-(3 y(x)+3) y'(x)+y(x)=0$$ [_rational, _dAlembert] Solution method Clairaut’s equation and related types, $$f(y-x y', y')=0$$ Maple ✓Mathematica ✓ ODE 888 $$4 x y'(x)^2=(a-3 x)^2$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 889 $$4 x y'(x)^2+2 x y'(x)-y(x)=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 890 $$4 x y'(x)^2-3 y(x) y'(x)+3=0$$ [[_homogeneous, class G], _rational, _dAlembert] Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s) Maple ✓Mathematica ✓ ODE 891 $$4 x y'(x)^2+4 y(x) y'(x)=1$$ [[_homogeneous, class G], _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 892 $$4 y(x) y'(x)+4 x y'(x)^2-y(x)^4=0$$ [[_homogeneous, class G]] Solution method No Missing Variables ODE, Solve for $$x$$ Maple ✓Mathematica ✓ ODE 893 $$4 (2-x) y'(x)^2+1=0$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 894 $$8 y(x) y'(x)+16 x y'(x)^2+y(x)^6=0$$ [[_homogeneous, class G]] Solution method No Missing Variables ODE, Solve for $$x$$ Maple ✓Mathematica ✓ ODE 895 $$x^2 y'(x)^2=a^2$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 896 $$x^2 y'(x)^2=y(x)^2$$ [_separable] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 897 $$x^2 y'(x)^2+x^2-y(x)^2=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 898 $$x^2 y'(x)^2=(x-y(x))^2$$ [_linear] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 899 $$x^2 y'(x)^2-y(x)^4+y(x)^2=0$$ [_separable] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 900 $$x^2 y'(x)^2-x y'(x)+(1-y(x)) y(x)=0$$ [_separable] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 901 $$a^2+2 a x y'(x)-2 a y(x)+x^2 y'(x)^2+x^2=0$$ [_rational] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 902 $$x^2 y'(x)^2-2 x y(x) y'(x)+y(x) (y(x)+1)-x=0$$ [[_1st_order, _with_linear_symmetries], _rational] Solution method Change of variable Maple ✓Mathematica ✓ ODE 903 $$-x^4+x^2 y'(x)^2+\left (1-x^2\right ) y(x)^2-2 x y(x) y'(x)=0$$ [_rational, [_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] Solution method Change of variable Maple ✓Mathematica ✓ ODE 904 $$x^2 y'(x)^2-(2 x y(x)+1) y'(x)+y(x)^2+1=0$$ [[_1st_order, _with_linear_symmetries], _rational, _Clairaut] Solution method Clairaut’s equation and related types, $$f(y-x y', y')=0$$ Maple ✓Mathematica ✓ ODE 905 $$-(a+2 x y(x)) y'(x)+x^2 y'(x)^2+y(x)^2=0$$ [[_homogeneous, class G], _rational, _Clairaut] Solution method Clairaut’s equation and related types, $$f(y-x y', y')=0$$ Maple ✓Mathematica ✓ ODE 906 $$x^2 y'(x)^2-x (x-2 y(x)) y'(x)+y(x)^2=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Change of variable Maple ✓Mathematica ✓ ODE 907 $$-4 a+x^2 y'(x)^2+2 x (y(x)+2 x) y'(x)+y(x)^2=0$$ [[_1st_order, _with_symmetry_[F(x),G(y)]]] Solution method Change of variable Maple ✓Mathematica ✓ ODE 908 $$x \left (x^3-2 y(x)\right ) y'(x)-\left (2 x^3-y(x)\right ) y(x)+x^2 y'(x)^2=0$$ [[_homogeneous, class G], _rational] Solution method Change of variable Maple ✓Mathematica ✓ ODE 909 $$x^2 y'(x)^2+3 x y(x) y'(x)+2 y(x)^2=0$$ [_separable] Solution method Homogeneous ODE, $$x^n f\left (\frac {y}{x} , y' \right )=0$$, Solve for $$p$$ Maple ✓Mathematica ✓ ODE 910 $$x^3+x^2 y'(x)^2-3 x y(x) y'(x)+2 y(x)^2=0$$ [[_homogeneous, class G], _rational] Solution method Change of variable Maple ✓Mathematica ✓ ODE 911 $$x^2 y'(x)^2+4 x y(x) y'(x)-5 y(x)^2=0$$ [_separable] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 912 $$x^2 y'(x)^2-4 x (y(x)+2) y'(x)+4 y(x) (y(x)+2)=0$$ [_separable] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 913 $$x^2 y'(x)^2-5 x y(x) y'(x)+6 y(x)^2=0$$ [_separable] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 914 $$x^2 y'(x)^2+x \left (x^2+x y(x)-2 y(x)\right ) y'(x)+(1-x) \left (x^2-y(x)\right ) y(x)=0$$ [_rational] Solution method Change of variable Maple ✗Mathematica ✗ ODE 915 $$x^2 y'(x)^2+(y(x)+2 x) y(x) y'(x)+y(x)^2=0$$ [[_homogeneous, class A], _dAlembert] Solution method Change of variable Maple ✓Mathematica ✓ ODE 916 $$x^2 y'(x)^2+(2 x-y(x)) y(x) y'(x)+y(x)^2=0$$ [[_homogeneous, class A], _dAlembert] Solution method No Missing Variables ODE, Solve for $$x$$ Maple ✓Mathematica ✓ ODE 917 $$y'(x) \left (a+b x^2 y(x)^3\right )+a b y(x)^3+x^2 y'(x)^2=0$$ [_quadrature] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 918 $$\left (1-x^2\right ) y'(x)^2=1-y(x)^2$$ [_rational, [_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✗Mathematica ✓ ODE 919 $$\left (1-x^2\right ) y'(x)^2+4 x^2+2 x y(x) y'(x)=0$$ [[_1st_order, _with_symmetry_[F(x),G(y)]]] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 920 $$\left (a^2+x^2\right ) y'(x)^2=b^2$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 921 $$\left (a^2-x^2\right ) y'(x)^2+b^2=0$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 922 $$\left (a^2-x^2\right ) y'(x)^2=b^2$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 923 $$\left (a^2-x^2\right ) y'(x)^2=x^2$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 924 $$\left (a^2-x^2\right ) y'(x)^2+x^2+2 x y(x) y'(x)=0$$ [[_1st_order, _with_symmetry_[F(x),G(y)]]] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 925 $$\left (a^2-x^2\right ) y'(x)^2-2 x y(x) y'(x)-y(x)^2=0$$ [_separable] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 926 $$\left (a^2+x^2\right ) y'(x)^2+b-2 x y(x) y'(x)+y(x)^2=0$$ [[_1st_order, _with_linear_symmetries], _rational, _Clairaut] Solution method Clairaut’s equation and related types, $$f(y-x y', y')=0$$ Maple ✓Mathematica ✓ ODE 927 $$\left (2 x^2+1\right ) y'(x)^2+\left (x^2+2 x y(x)+y(x)^2+2\right ) y'(x)+2 y(x)^2+1=0$$ [y=_G(x,y')] Solution method Change of variable Maple ✗Mathematica ✓ ODE 928 $$4 x^2 y'(x)^2-4 x y(x) y'(x)=8 x^3-y(x)^2$$ [_linear] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 929 $$a x^2 y'(x)^2+(1-a) a x^2-2 a x y(x) y'(x)+y(x)^2=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous ODE, $$x^n f\left (\frac {y}{x} , y' \right )=0$$, Solve for $$p$$ Maple ✓Mathematica ✓ ODE 930 $$\left (1-a^2\right ) x^2 y'(x)^2-a^2 x^2-2 x y(x) y'(x)+y(x)^2=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 931 $$x^3 y'(x)^2=a$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 932 $$x^3 y'(x)^2+x y'(x)-y(x)=0$$ [[_homogeneous, class G], _rational] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✗Mathematica ✓ ODE 933 $$a+x^3 y'(x)^2+x^2 y(x) y'(x)=0$$ [[_homogeneous, class G], _rational] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 934 $$x^3 y'(x)^2-\left (2 x^2 y(x)+1\right ) y'(x)+x y(x)^2=0$$ [[_homogeneous, class G], _rational] Solution method Change of variable Maple ✓Mathematica ✓ ODE 935 $$x \left (1-x^2\right ) y'(x)^2-2 \left (1-x^2\right ) y(x) y'(x)+x \left (1-y(x)^2\right )=0$$ [_rational, [_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] Solution method Change of variable Maple ✓Mathematica ✓ ODE 936 $$4 x (a-x) (b-x) y'(x)^2=\left (-2 x (a+b)+a b+2 x^2\right )^2$$ [_quadrature] Solution method Change of variable Maple ✓Mathematica ✓ ODE 937 $$x^4 y'(x)^2-x y'(x)-y(x)=0$$ [[_homogeneous, class G], _rational] Solution method Homogeneous ODE, The Isobaric equation Maple ✓Mathematica ✓ ODE 938 $$x^4 y'(x)^2+2 x^3 y(x) y'(x)-4=0$$ [[_homogeneous, class G], _rational] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 939 $$x^4 y'(x)^2+x y(x)^2 y'(x)-y(x)^3=0$$ [[_homogeneous, class G]] Solution method Change of variable Maple ✓Mathematica ✓ ODE 940 $$x^2 \left (a^2-x^2\right ) y'(x)^2+1=0$$ [_quadrature] Solution method Missing Variables ODE, Dependent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 941 $$3 x^4 y'(x)^2-x y(x)-y(x)=0$$ [_rational, [_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 942 $$4 x^5 y'(x)^2+12 x^4 y(x) y'(x)+9=0$$ [[_homogeneous, class G]] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 943 $$x^6 y'(x)^2-2 x y'(x)-4 y(x)=0$$ [[_homogeneous, class G], _rational] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 944 $$x^8 y'(x)^2+3 x y'(x)+9 y(x)=0$$ [[_homogeneous, class G]] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 945 $$y(x) y'(x)^2=a$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 946 $$y(x) y'(x)^2=a^2 x$$ [[_homogeneous, class A], _dAlembert] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 947 $$y(x) y'(x)^2=e^{2 x}$$ [[_1st_order, _with_linear_symmetries]] Solution method Change of variable Maple ✓Mathematica ✓ ODE 948 $$2 a x y'(x)-a y(x)+y(x) y'(x)^2=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method Homogeneous ODE, $$x^n f\left (\frac {y}{x} , y' \right )=0$$ Maple ✓Mathematica ✓ ODE 949 $$-4 a^2 x y'(x)+a^2 y(x)+y(x) y'(x)^2=0$$ [[_homogeneous, class A], _dAlembert] Solution method No Missing Variables ODE, Solve for $$x$$ Maple ✓Mathematica ✓ ODE 950 $$a x y'(x)+b y(x)+y(x) y'(x)^2=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for $$x$$ Maple ✓Mathematica ✓ ODE 951 $$-(a-2 b x) y'(x)-b y(x)+y(x) y'(x)^2=0$$ [[_homogeneous, class C], _rational, _dAlembert] Solution method Change of variable Maple ✓Mathematica ✓ ODE 952 $$x^3 y'(x)-x^2 y(x)+y(x) y'(x)^2=0$$ [[_1st_order, _with_linear_symmetries]] Solution method Change of variable Maple ✓Mathematica ✓ ODE 953 $$y(x) y'(x)^2+(x-y(x)) y'(x)-x=0$$ [_quadrature] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 954 $$y(x) y'(x)^2-(y(x)+x) y'(x)+y(x)=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for $$x$$ Maple ✓Mathematica ✓ ODE 955 $$y(x) y'(x)^2-(x y(x)+1) y'(x)+x=0$$ [_quadrature] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 956 $$y(x) y'(x)^2+\left (x-y(x)^2\right ) y'(x)-x y(x)=0$$ [_quadrature] Solution method No Missing Variables ODE, Solve for $$y'$$ Maple ✓Mathematica ✓ ODE 957 $$y(x) y'(x)^2+y(x)=a$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Use new variable Maple ✓Mathematica ✓ ODE 958 $$(y(x)+x) y'(x)^2+2 x y'(x)-y(x)=0$$ [[_homogeneous, class A], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 959 $$(2 x-y(x)) y'(x)^2-2 (1-x) y'(x)-y(x)+2=0$$ [[_homogeneous, class C], _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 960 $$2 y(x) y'(x)^2+(5-4 x) y'(x)+2 y(x)=0$$ [[_homogeneous, class C], _rational, _dAlembert] Solution method No Missing Variables ODE, Solve for $$y$$ Maple ✓Mathematica ✓ ODE 961 $$4 x^3 y'(x)-4 x^2 y(x)+9 y(x) y'(x)^2=0$$ [[_1st_order, _with_linear_symmetries]] Solution method Change of variable Maple ✓Mathematica ✓ ODE 962 $$(1-a y(x)) y'(x)^2=a y(x)$$ [_quadrature] Solution method Missing Variables ODE, Independent variable missing, Use new variable Maple ✓Mathematica ✓ ODE 963 $$y'(x)^2 (\text {a0}+\text {b0} x+\text {c0} y(x))+y'(x) (\text {a1}+\text {b1} x+\text {c1} y(x))+\text {a2}+\text {b2} x+\text {c2} y(x)=0$$ [_rational, _dAlembert] Solution method Change of variable Maple ✓Mathematica ✓ ODE 964 $$\left (x^2-a y(x)\right ) y'(x)^2-2 x y(x) y'(x)=0$$ [_quadrature]