| # | ODE | Mathematica | Maple | Sympy |
| \[
{} a y \left (y-1\right ) y^{\prime \prime }+\left (b y+c \right ) {y^{\prime }}^{2}+h \left (y\right ) = 0
\]
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| \[
{} a y \left (y-1\right ) y^{\prime \prime }-\left (a -1\right ) \left (2 y-1\right ) {y^{\prime }}^{2}+f y \left (y-1\right ) y^{\prime } = 0
\]
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| \[
{} a b y \left (y-1\right ) y^{\prime \prime }-\left (\left (2 a b -a -b \right ) y+\left (1-a \right ) b \right ) {y^{\prime }}^{2}+f y \left (y-1\right ) y^{\prime } = 0
\]
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| \[
{} x y^{2} y^{\prime \prime }-a = 0
\]
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| \[
{} \left (a^{2}-x^{2}\right ) \left (a^{2}-y^{2}\right ) y^{\prime \prime }+\left (a^{2}-x^{2}\right ) y {y^{\prime }}^{2}-x \left (a^{2}-y^{2}\right ) y^{\prime } = 0
\]
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| \[
{} 2 x^{2} y \left (y-1\right ) y^{\prime \prime }-x^{2} \left (3 y-1\right ) {y^{\prime }}^{2}+2 x y \left (y-1\right ) y^{\prime }+\left (a y^{2}+b \right ) \left (y-1\right )^{3}+c x y^{2} \left (y-1\right )+d \,x^{2} y^{2} \left (1+y\right ) = 0
\]
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| \[
{} \left (x +y\right ) \left (x y^{\prime }-y\right )^{3}+x^{3} y^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (1-3 y^{2}\right ) {y^{\prime }}^{2}+y \left (1+y^{2}\right ) y^{\prime \prime } = 0
\]
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| \[
{} 2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1 = 0
\]
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| \[
{} 2 y^{3} y^{\prime \prime }+y^{2} {y^{\prime }}^{2}-x^{2} a -b x -c = 0
\]
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| \[
{} 2 \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) y^{\prime \prime }-\left (\left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )+\left (y-b \right ) \left (y-c \right )\right ) {y^{\prime }}^{2}+\left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} \left (A_{0} +\frac {B_{0}}{\left (y-a \right )^{2}}+\frac {C_{1}}{\left (y-b \right )^{2}}+\frac {D_{0}}{\left (y-c \right )^{2}}\right ) = 0
\]
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| \[
{} \left (4 y^{3}-a y-b \right ) y^{\prime \prime }-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2} = 0
\]
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| \[
{} \left (4 y^{3}-a y-b \right ) \left (y^{\prime \prime }+f y^{\prime }\right )-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2} = 0
\]
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| \[
{} \left (y^{2}-1\right ) \left (a^{2} y^{2}-1\right ) y^{\prime \prime }+b \sqrt {\left (1-y^{2}\right ) \left (1-a^{2} y^{2}\right )}\, {y^{\prime }}^{2}+\left (1+a^{2}-2 a^{2} y^{2}\right ) y {y^{\prime }}^{2} = 0
\]
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| \[
{} \left (c +2 b x +x^{2} a +y^{2}\right )^{2} y^{\prime \prime }+y d = 0
\]
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| \[
{} \sqrt {y}\, y^{\prime \prime }-a = 0
\]
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| \[
{} \sqrt {x^{2}+y^{2}}\, y^{\prime \prime }-a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\]
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| \[
{} \left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime } = 0
\]
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| \[
{} \left (b +a \sin \left (y\right )^{2}\right ) y^{\prime \prime }+a {y^{\prime }}^{2} \cos \left (y\right ) \sin \left (y\right )+A y \left (c +a \sin \left (y\right )^{2}\right ) = 0
\]
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| \[
{} h \left (y\right ) y^{\prime \prime }+a h \left (y\right ) {y^{\prime }}^{2}+j \left (y\right ) = 0
\]
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| \[
{} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2} = 0
\]
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| \[
{} \left (x y^{\prime }-y\right ) y^{\prime \prime }+4 {y^{\prime }}^{2} = 0
\]
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| \[
{} \left (x y^{\prime }-y\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right )^{2} = 0
\]
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| \[
{} a \,x^{3} y^{\prime } y^{\prime \prime }+b y^{2} = 0
\]
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| \[
{} y+3 x y^{\prime }+2 {y^{\prime }}^{3} y+\left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime } = 0
\]
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| \[
{} y^{3}+\left ({y^{\prime }}^{2}+y^{2}\right ) y^{\prime \prime } = 0
\]
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| \[
{} \left ({y^{\prime }}^{2}+a \left (x y^{\prime }-y\right )\right ) y^{\prime \prime }-b = 0
\]
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| \[
{} \left (a \sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }\right ) y^{\prime \prime }-{y^{\prime }}^{2}-1 = 0
\]
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| \[
{} {y^{\prime \prime }}^{2}-a y-b = 0
\]
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| \[
{} a^{2} {y^{\prime \prime }}^{2}-2 a x y^{\prime \prime }+y^{\prime } = 0
\]
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| \[
{} 2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2}-x \left (x +4 y^{\prime }\right ) y^{\prime \prime }+2 \left (x +y^{\prime }\right ) y^{\prime }-2 y = 0
\]
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| \[
{} 4 {y^{\prime }}^{2}-2 \left (3 x y^{\prime }+y\right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2} = 0
\]
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✓ |
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| \[
{} \left (2-9 x \right ) x^{2} {y^{\prime \prime }}^{2}-6 \left (1-6 x \right ) x y^{\prime } y^{\prime \prime }+6 y y^{\prime \prime }-36 x {y^{\prime }}^{2} = 0
\]
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| \[
{} y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x} = 0
\]
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| \[
{} \left (a^{2} y^{2}-b^{2}\right ) {y^{\prime \prime }}^{2}-2 a^{2} y {y^{\prime }}^{2} y^{\prime \prime }+\left (a^{2} {y^{\prime }}^{2}-1\right ) {y^{\prime }}^{2} = 0
\]
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| \[
{} \left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2}-4 x y \left (x y^{\prime }-y\right )^{3} = 0
\]
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| \[
{} 32 y^{\prime \prime } \left (x y^{\prime \prime }-y^{\prime }\right )^{3}+\left (2 y y^{\prime \prime }-{y^{\prime }}^{2}\right )^{3} = 0
\]
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| \[
{} \sqrt {a {y^{\prime \prime }}^{2}+b {y^{\prime }}^{2}}+c y y^{\prime \prime }+d {y^{\prime }}^{2} = 0
\]
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| \[
{} y^{\prime \prime \prime }-a^{2} \left ({y^{\prime }}^{5}+2 {y^{\prime }}^{3}+y^{\prime }\right ) = 0
\]
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| \[
{} y^{\prime \prime \prime }+y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0
\]
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| \[
{} y^{\prime \prime \prime }-y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\]
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| \[
{} a y y^{\prime \prime }+y^{\prime \prime \prime } = 0
\]
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| \[
{} x^{2} y^{\prime \prime \prime }+x y^{\prime \prime }+\left (2 x y-1\right ) y^{\prime }+y^{2}-f \left (x \right ) = 0
\]
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| \[
{} x^{2} y^{\prime \prime \prime }+x \left (y-1\right ) y^{\prime \prime }+x {y^{\prime }}^{2}+\left (1-y\right ) y^{\prime } = 0
\]
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| \[
{} y^{3} y^{\prime }-y^{\prime } y^{\prime \prime }+y y^{\prime \prime \prime } = 0
\]
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| \[
{} 15 {y^{\prime }}^{3}-18 y y^{\prime } y^{\prime \prime }+4 y^{2} y^{\prime \prime \prime } = 0
\]
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✓ |
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| \[
{} 40 {y^{\prime }}^{3}-45 y y^{\prime } y^{\prime \prime }+9 y^{2} y^{\prime \prime \prime } = 0
\]
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| \[
{} \left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }-3 y^{\prime } {y^{\prime \prime }}^{2} = 0
\]
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| \[
{} \left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }-\left (a +3 y^{\prime }\right ) {y^{\prime \prime }}^{2} = 0
\]
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| \[
{} y^{\prime \prime } y^{\prime \prime \prime }-a \sqrt {1+b^{2} {y^{\prime \prime }}^{2}} = 0
\]
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| \[
{} y^{\prime } y^{\prime \prime \prime \prime }-y^{\prime \prime } y^{\prime \prime \prime }+{y^{\prime }}^{3} y^{\prime \prime \prime } = 0
\]
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| \[
{} 3 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2} = 0
\]
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| \[
{} 9 {y^{\prime \prime }}^{2} y^{\left (5\right )}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+40 y^{\prime \prime \prime } = 0
\]
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| \[
{} y^{\prime \prime }-f \left (y\right ) = 0
\]
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| \[
{} y^{\prime \prime \prime } = f \left (y\right )
\]
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| \[
{} [x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )+y \left (t \right ) = {\mathrm e}^{2 t}+t, x^{\prime }\left (t \right )-x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right ) = {\mathrm e}^{t}-1]
\]
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| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+y \left (t \right ) = f \left (t \right ), x^{\prime \prime }\left (t \right )+y^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )+y \left (t \right ) = g \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right )-x \left (t \right )+2 y \left (t \right ) = 0, x^{\prime \prime }\left (t \right )-2 y^{\prime }\left (t \right ) = 2 t -\cos \left (2 t \right )]
\]
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| \[
{} [t x^{\prime }\left (t \right )-t y^{\prime }\left (t \right )-2 y \left (t \right ) = 0, t x^{\prime \prime }\left (t \right )+2 x^{\prime }\left (t \right )+t x \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime \prime }\left (t \right ) = a_{1} x \left (t \right )+b_{1} y \left (t \right )+c_{1}, y^{\prime \prime }\left (t \right ) = a_{2} x \left (t \right )+b_{2} y \left (t \right )+c_{2}]
\]
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| \[
{} \left [x^{\prime \prime }\left (t \right ) = \left (3 \cos \left (a t +b \right )^{2}-1\right ) c^{2} x \left (t \right )+\frac {3 c^{2} y \left (t \right ) \sin \left (2 a t b \right )}{2}, y^{\prime \prime }\left (t \right ) = \left (3 \sin \left (a t +b \right )^{2}-1\right ) c^{2} y \left (t \right )+\frac {3 c^{2} x \left (t \right ) \sin \left (2 a t b \right )}{2}\right ]
\]
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| \[
{} [a_{1} x^{\prime \prime }\left (t \right )+b_{1} x^{\prime }\left (t \right )+c_{1} x \left (t \right )-A y^{\prime }\left (t \right ) = B \,{\mathrm e}^{i \omega t}, a_{2} y^{\prime \prime }\left (t \right )+b_{2} y^{\prime }\left (t \right )+c_{2} y \left (t \right )+A x^{\prime }\left (t \right ) = 0]
\]
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| \[
{} [x^{\prime \prime }\left (t \right )+a \left (x^{\prime }\left (t \right )-y^{\prime }\left (t \right )\right )+b_{1} x \left (t \right ) = c_{1} {\mathrm e}^{i \omega t}, y^{\prime \prime }\left (t \right )+a \left (y^{\prime }\left (t \right )-x^{\prime }\left (t \right )\right )+b_{2} y \left (t \right ) = c_{2} {\mathrm e}^{i \omega t}]
\]
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| \[
{} [\operatorname {a11} x^{\prime \prime }\left (t \right )+\operatorname {b11} x^{\prime }\left (t \right )+\operatorname {c11} x \left (t \right )+\operatorname {a12} y^{\prime \prime }\left (t \right )+\operatorname {b12} y^{\prime }\left (t \right )+\operatorname {c12} y \left (t \right ) = 0, \operatorname {a21} x^{\prime \prime }\left (t \right )+\operatorname {b21} x^{\prime }\left (t \right )+\operatorname {c21} x \left (t \right )+\operatorname {a22} y^{\prime \prime }\left (t \right )+\operatorname {b22} y^{\prime }\left (t \right )+\operatorname {c22} y \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 6 x \left (t \right )-72 y \left (t \right )+44 z \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-4 y \left (t \right )+26 z \left (t \right ), z^{\prime }\left (t \right ) = 6 x \left (t \right )-63 y \left (t \right )+38 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = a x \left (t \right )+g y \left (t \right )+\beta z \left (t \right ), y^{\prime }\left (t \right ) = g x \left (t \right )+b y \left (t \right )+\alpha z \left (t \right ), z^{\prime }\left (t \right ) = \beta x \left (t \right )+\alpha y \left (t \right )+c z \left (t \right )]
\]
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| \[
{} [t x^{\prime }\left (t \right ) = 2 x \left (t \right )-t, t^{3} y^{\prime }\left (t \right ) = -x \left (t \right )+t^{2} y \left (t \right )+t, t^{4} z^{\prime }\left (t \right ) = -x \left (t \right )-t^{2} y \left (t \right )+t^{3} z \left (t \right )+t]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = a x_{2} \left (t \right )+b x_{3} \left (t \right ) \cos \left (c t \right )+b x_{4} \left (t \right ) \sin \left (c t \right ), x_{2}^{\prime }\left (t \right ) = -a x_{1} \left (t \right )+b x_{3} \left (t \right ) \sin \left (c t \right )-b x_{4} \left (t \right ) \cos \left (c t \right ), x_{3}^{\prime }\left (t \right ) = -b x_{1} \left (t \right ) \cos \left (c t \right )-b x_{2} \left (t \right ) \sin \left (c t \right )+a x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -b x_{1} \left (t \right ) \sin \left (c t \right )+b x_{2} \left (t \right ) \cos \left (c t \right )-a x_{3} \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ) \left (x \left (t \right )+y \left (t \right )\right ), y^{\prime }\left (t \right ) = y \left (t \right ) \left (x \left (t \right )+y \left (t \right )\right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = \left (a y \left (t \right )+b \right ) x \left (t \right ), y^{\prime }\left (t \right ) = \left (c x \left (t \right )+d \right ) y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ) \left (a \left (p x \left (t \right )+q y \left (t \right )\right )+\alpha \right ), y^{\prime }\left (t \right ) = y \left (t \right ) \left (\beta +b \left (p x \left (t \right )+q y \left (t \right )\right )\right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = h \left (a -x \left (t \right )\right ) \left (c -x \left (t \right )-y \left (t \right )\right ), y^{\prime }\left (t \right ) = k \left (b -y \left (t \right )\right ) \left (c -x \left (t \right )-y \left (t \right )\right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right )^{2}-\cos \left (x \left (t \right )\right ), y^{\prime }\left (t \right ) = -y \left (t \right ) \sin \left (x \left (t \right )\right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ) y \left (t \right )^{2}+x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right ) x \left (t \right )^{2}-x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )-y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -y \left (t \right )+x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}-1\right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}-1\right )]
\]
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| \[
{} [\left (x \left (t \right )^{2}+y \left (t \right )^{2}-t^{2}\right ) x^{\prime }\left (t \right ) = -2 t x \left (t \right ), \left (x \left (t \right )^{2}+y \left (t \right )^{2}-t^{2}\right ) y^{\prime }\left (t \right ) = -2 t y \left (t \right )]
\]
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| \[
{} \left [x^{\prime \prime }\left (t \right ) = a \,{\mathrm e}^{2 x \left (t \right )}-{\mathrm e}^{-x \left (t \right )}+{\mathrm e}^{-2 x \left (t \right )} \cos \left (y \left (t \right )\right )^{2}, y^{\prime \prime }\left (t \right ) = {\mathrm e}^{-2 x \left (t \right )} \sin \left (y \left (t \right )\right ) \cos \left (y \left (t \right )\right )-\frac {\sin \left (y \left (t \right )\right )}{\cos \left (y \left (t \right )\right )^{3}}\right ]
\]
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| \[
{} \left [x^{\prime \prime }\left (t \right ) = \frac {k x \left (t \right )}{\left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )^{{3}/{2}}}, y^{\prime \prime }\left (t \right ) = \frac {k y \left (t \right )}{\left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )^{{3}/{2}}}\right ]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )^{2}+z \left (t \right )]
\]
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|
| \[
{} [a x^{\prime }\left (t \right ) = \left (b -c \right ) y \left (t \right ) z \left (t \right ), b y^{\prime }\left (t \right ) = \left (c -a \right ) z \left (t \right ) x \left (t \right ), c z^{\prime }\left (t \right ) = \left (a -b \right ) x \left (t \right ) y \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ) \left (y \left (t \right )-z \left (t \right )\right ), y^{\prime }\left (t \right ) = y \left (t \right ) \left (-x \left (t \right )+z \left (t \right )\right ), z^{\prime }\left (t \right ) = z \left (t \right ) \left (x \left (t \right )-y \left (t \right )\right )]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right )+z^{\prime }\left (t \right ) = y \left (t \right ) z \left (t \right ), x^{\prime }\left (t \right )+z^{\prime }\left (t \right ) = x \left (t \right ) z \left (t \right )]
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left [x^{\prime }\left (t \right ) = \frac {x \left (t \right )^{2}}{2}-\frac {y \left (t \right )}{24}, y^{\prime }\left (t \right ) = 2 x \left (t \right ) y \left (t \right )-3 z \left (t \right ), z^{\prime }\left (t \right ) = 3 x \left (t \right ) z \left (t \right )-\frac {y \left (t \right )^{2}}{6}\right ]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ) \left (y \left (t \right )^{2}-z \left (t \right )^{2}\right ), y^{\prime }\left (t \right ) = y \left (t \right ) \left (z \left (t \right )^{2}-x \left (t \right )^{2}\right ), z^{\prime }\left (t \right ) = z \left (t \right ) \left (x \left (t \right )^{2}-y \left (t \right )^{2}\right )]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ) \left (y \left (t \right )^{2}-z \left (t \right )^{2}\right ), y^{\prime }\left (t \right ) = -y \left (t \right ) \left (z \left (t \right )^{2}+x \left (t \right )^{2}\right ), z^{\prime }\left (t \right ) = z \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )]
\]
|
✗ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ) y \left (t \right )^{2}+x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right ) x \left (t \right )^{2}-x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = y \left (t \right )^{2}-x \left (t \right )^{2}]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [\left (x \left (t \right )-y \left (t \right )\right ) \left (x \left (t \right )-z \left (t \right )\right ) x^{\prime }\left (t \right ) = f \left (t \right ), \left (-x \left (t \right )+y \left (t \right )\right ) \left (y \left (t \right )-z \left (t \right )\right ) y^{\prime }\left (t \right ) = f \left (t \right ), \left (-x \left (t \right )+z \left (t \right )\right ) \left (-y \left (t \right )+z \left (t \right )\right ) z^{\prime }\left (t \right ) = f \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a y^{2}+b x +c
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}-a^{2} x^{2}+3 a
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+a^{2} x^{2}+b x +c
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a y^{2}+b \,x^{n}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+a n \,x^{n -1}-a^{2} x^{2 n}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a y^{2}+b \,x^{2 n}+c \,x^{n -1}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a \,x^{n} y^{2}+b \,x^{-n -2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a \,x^{n} y^{2}+b \,x^{m}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = y^{2}+k \left (a x +b \right )^{n} \left (c x +d \right )^{-n -4}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = a \,x^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{n +2 m}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \left (a \,x^{2 n}+b \,x^{n -1}\right ) y^{2}+c
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0} x +b_{0} = 0
\]
|
✓ |
✓ |
✗ |
|