| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x y^{\prime }-y&=x \sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.521 |
|
| \begin{align*}
\ln \left (y\right ) y+x y^{\prime }&=y x \,{\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.415 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.537 |
|
| \begin{align*}
x \left (-a^{2}+x^{2}+y^{2}\right )+y \left (x^{2}-y^{2}-b^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.608 |
|
| \begin{align*}
y^{\prime }&=\frac {1+x^{2}+y^{2}}{2 x y} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.303 |
|
| \begin{align*}
y y^{\prime }+x&=m \left (x y^{\prime }-y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
12.541 |
|
| \begin{align*}
y+\left (y^{n} a \,x^{2}-2 x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
8.182 |
|
| \begin{align*}
y \left (2 x^{2} y+{\mathrm e}^{x}\right )-\left ({\mathrm e}^{x}+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
2.727 |
|
| \begin{align*}
{x^{\prime }}^{2}&=k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right ) \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
4.583 |
|
| \begin{align*}
y y^{\prime }+b y^{2}&=a \cos \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.178 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3 x -2 y}+x^{2} {\mathrm e}^{-2 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.210 |
|
| \begin{align*}
x^{2}+y^{2}+x -\left (2 x^{2}+2 y^{2}-y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
2.094 |
|
| \begin{align*}
2 y+3 x y^{\prime }+2 x y \left (3 y+4 x y^{\prime }\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
38.772 |
|
| \begin{align*}
y \left (1+\frac {1}{x}\right )+\cos \left (y\right )+\left (x +\ln \left (x \right )-\sin \left (y\right ) x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
28.800 |
|
| \begin{align*}
\left (2 x +2 y+3\right ) y^{\prime }&=x +y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.525 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (2 \ln \left (x \right )+1\right ) x}{\sin \left (y\right )+y \cos \left (y\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.824 |
|
| \begin{align*}
s^{\prime }+x^{2}&=x^{2} {\mathrm e}^{3 s} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.134 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \left ({\mathrm e}^{x}-{\mathrm e}^{y}\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
✓ |
✓ |
✓ |
9.343 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x +y\right )+\cos \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
52.549 |
|
| \begin{align*}
y^{\prime }+\frac {\tan \left (y\right )}{x}&=\frac {\tan \left (y\right ) \sin \left (y\right )}{x^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
35.943 |
|
| \begin{align*}
x^{2}-a y&=\left (a x -y^{2}\right ) y^{\prime } \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
1.846 |
|
| \begin{align*}
y \left ({\mathrm e}^{x}+2 y x \right )-{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.383 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
15.824 |
|
| \begin{align*}
y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
6.691 |
|
| \begin{align*}
y-x y^{\prime }+x^{2}+1+x^{2} \sin \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
✗ |
2.701 |
|
| \begin{align*}
\sec \left (y\right )^{2} y^{\prime }+2 x \tan \left (y\right )&=x^{3} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✗ |
✓ |
✗ |
4.013 |
|
| \begin{align*}
y^{\prime }+\frac {a x +b y+c}{b x +f y+e}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
72.490 |
|
| \begin{align*}
y^{\prime \prime }-n^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.496 |
|
| \begin{align*}
2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| \begin{align*}
2 x^{\prime \prime }+5 x^{\prime }-12 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }-54 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.275 |
|
| \begin{align*}
9 x^{\prime \prime }+18 x^{\prime }-16 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.291 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+3 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.334 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.055 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.066 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-5 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.057 |
|
| \begin{align*}
2 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.061 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| \begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.064 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{4 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
y^{\prime \prime }-y&=2+5 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-15 y&=15 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.430 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{\frac {5 x}{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| \begin{align*}
y^{\prime \prime }+2 p y^{\prime }+\left (p^{2}+q^{2}\right ) y&={\mathrm e}^{k x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\cos \left (2 x \right )+\sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} y&=\cos \left (a x \right )+\cos \left (b x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.737 |
|
| \begin{align*}
4 y+y^{\prime \prime }&={\mathrm e}^{x}+\sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-12 y&=\cos \left (4 x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.189 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=2 \sin \left (\frac {x}{2}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.414 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (3 x \right )-\cos \left (\frac {x}{2}\right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.093 |
|
| \begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=x \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-6 y^{\prime }&=x^{2}+1 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.124 |
|
| \begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{2 x}+x^{2}+x \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.139 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime \prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.118 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+4 y&={\mathrm e}^{x} \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
y^{\prime \prime }-y&=\cos \left (x \right ) \cosh \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.745 |
|
| \begin{align*}
y^{\prime \prime \prime }-7 y^{\prime }-6 y&={\mathrm e}^{2 x} \left (x +1\right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.127 |
|
| \begin{align*}
y+y^{\prime \prime }+y^{\prime \prime \prime \prime }&=a \,x^{2}+b \,{\mathrm e}^{-x} \sin \left (2 x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.957 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }-12 y&=\left (x -1\right ) {\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=x^{2} \cos \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=x \sin \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \sin \left (x \right ) x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=8 x^{2} {\mathrm e}^{2 x} \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.854 |
|
| \begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{-x}+\cos \left (x \right )+x^{3}+{\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.529 |
|
| \begin{align*}
y+y^{\prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.311 |
|
| \begin{align*}
y^{\left (6\right )}-2 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+3 y^{\prime \prime }-2 y^{\prime }+y&=\sin \left (\frac {x}{2}\right )^{2}+{\mathrm e}^{x} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.512 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y&=16 x^{2}+256 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.183 |
|
| \begin{align*}
y^{\prime \prime }+y&=3 \cos \left (x \right )^{2}+2 \sin \left (x \right )^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.594 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y&=96 \sin \left (2 x \right ) \cos \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.741 |
|
| \begin{align*}
y^{\left (5\right )}-13 y^{\prime \prime \prime }+26 y^{\prime \prime }+82 y^{\prime }+104 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.078 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y+37 \sin \left (3 x \right )&=0 \\
y \left (\frac {\pi }{2}\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=24 x \cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 12 \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.748 |
|
| \begin{align*}
{y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.259 |
|
| \begin{align*}
{y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.267 |
|
| \begin{align*}
{y^{\prime }}^{2}-9 y^{\prime }+18&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.267 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }-3 x^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.510 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.049 |
|
| \begin{align*}
y^{\prime } \left (y^{\prime }-y\right )&=x \left (x +y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \begin{align*}
y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| \begin{align*}
x +y {y^{\prime }}^{2}&=\left (y x +1\right ) y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.429 |
|
| \begin{align*}
{y^{\prime }}^{2} x +\left (-x +y\right ) y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
{y^{\prime }}^{3}-a \,x^{4}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.990 |
|
| \begin{align*}
{y^{\prime }}^{2}+x y^{\prime }+y y^{\prime }+y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.515 |
|
| \begin{align*}
{y^{\prime }}^{3}-y^{\prime } \left (x^{2}+y x +y^{2}\right )+x y \left (x +y\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
\left (y^{\prime }+y+x \right ) \left (x y^{\prime }+x +y\right ) \left (y^{\prime }+2 x \right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{3}+y \left (x^{2} y+1\right ) {y^{\prime }}^{2}+y^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
16.929 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+x y y^{\prime }-6 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \begin{align*}
{y^{\prime }}^{3}+2 {y^{\prime }}^{2} x -y^{2} {y^{\prime }}^{2}-2 x y^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| \begin{align*}
\left (2-3 y\right )^{2} {y^{\prime }}^{2}&=4-4 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| \begin{align*}
y&=3 x +a \ln \left (y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.319 |
|
| \begin{align*}
{y^{\prime }}^{2}-y y^{\prime }+x&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.973 |
|
| \begin{align*}
y&=x +a \arctan \left (y^{\prime }\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.810 |
|