| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x \left (x +y\right ) y^{\prime \prime }+x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-y = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} 2 x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{2} \left (y-1\right ) y^{\prime \prime }-2 x^{2} {y^{\prime }}^{2}-2 x \left (y-1\right ) y^{\prime }-2 y \left (y-1\right )^{2} = 0
\]
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✗ |
✓ |
✗ |
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| \[
{} x^{2} \left (x +y\right ) y^{\prime \prime }-\left (x y^{\prime }-y\right )^{2} = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{2} \left (x -y\right ) y^{\prime \prime }+a \left (x y^{\prime }-y\right )^{2} = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} 2 x^{2} y y^{\prime \prime }-x^{2} \left (1+{y^{\prime }}^{2}\right )+y^{2} = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} a \,x^{2} y y^{\prime \prime }+b \,x^{2} {y^{\prime }}^{2}+c x y y^{\prime }+d y^{2} = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} x \left (1+x \right )^{2} y y^{\prime \prime }-x \left (1+x \right )^{2} {y^{\prime }}^{2}+2 \left (1+x \right )^{2} y y^{\prime }-a \left (x +2\right ) y^{2} = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} 8 \left (-x^{3}+1\right ) y y^{\prime \prime }-4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}-12 x^{2} y y^{\prime }+3 x y^{2} = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{2} y^{\prime \prime }-a = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} a x +y {y^{\prime }}^{2}+y^{2} y^{\prime \prime } = 0
\]
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✗ |
✓ |
✗ |
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| \[
{} y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}-a x -b = 0
\]
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✗ |
✓ |
✗ |
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| \[
{} \left (1-2 y\right ) {y^{\prime }}^{2}+\left (1+y^{2}\right ) y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (1+y^{2}\right ) y^{\prime \prime }-3 y {y^{\prime }}^{2} = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (x +y^{2}\right ) y^{\prime \prime }-2 \left (x -y^{2}\right ) {y^{\prime }}^{3}+y^{\prime } \left (1+4 y y^{\prime }\right ) = 0
\]
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✗ |
✓ |
✗ |
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| \[
{} \left (x^{2}+y^{2}\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right ) \left (x y^{\prime }-y\right ) = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (x^{2}+y^{2}\right ) y^{\prime \prime }-2 \left (1+{y^{\prime }}^{2}\right ) \left (x y^{\prime }-y\right ) = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} 2 \left (1-y\right ) y y^{\prime \prime }-\left (1-2 y\right ) {y^{\prime }}^{2}+f \left (x \right ) \left (1-y\right ) y y^{\prime } = 0
\]
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✓ |
✓ |
✗ |
|
| \[
{} 2 \left (1-y\right ) y y^{\prime \prime }-\left (1-3 y\right ) {y^{\prime }}^{2}+h \left (y\right ) = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} 3 \left (1-y\right ) y y^{\prime \prime }-2 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right ) = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} \left (1-y\right ) y^{\prime \prime }-3 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right ) = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} a y \left (y-1\right ) y^{\prime \prime }+\left (b y+c \right ) {y^{\prime }}^{2}+h \left (y\right ) = 0
\]
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✓ |
✓ |
✗ |
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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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✓ |
✓ |
✗ |
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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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✓ |
✓ |
✗ |
|
| \[
{} x y^{2} y^{\prime \prime }-a = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a^{2}-x^{2}\right ) \left (a^{2}-y^{2}\right ) y^{\prime \prime }+\left (a^{2}-x^{2}\right ) y {y^{\prime }}^{2}-x \left (a^{2}-y^{2}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x^{2} y \left (y-1\right ) y^{\prime \prime }-x^{2} \left (3 y-1\right ) {y^{\prime }}^{2}+2 x y \left (y-1\right ) y^{\prime }+\left (a y^{2}+b \right ) \left (y-1\right )^{3}+c x y^{2} \left (y-1\right )+d \,x^{2} y^{2} \left (1+y\right ) = 0
\]
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✗ |
✗ |
✗ |
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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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| \[
{} y^{3} y^{\prime \prime }-a = 0
\]
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✓ |
✓ |
✓ |
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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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✓ |
✓ |
✗ |
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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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✗ |
✗ |
✗ |
|
| \[
{} 2 \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) y^{\prime \prime }-\left (\left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )+\left (y-b \right ) \left (y-c \right )\right ) {y^{\prime }}^{2}+\left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} \left (A_{0} +\frac {B_{0}}{\left (y-a \right )^{2}}+\frac {C_{1}}{\left (y-b \right )^{2}}+\frac {D_{0}}{\left (y-c \right )^{2}}\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (4 y^{3}-a y-b \right ) y^{\prime \prime }-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (4 y^{3}-a y-b \right ) \left (y^{\prime \prime }+f y^{\prime }\right )-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2} = 0
\]
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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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✓ |
✓ |
✗ |
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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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✗ |
✓ |
✗ |
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| \[
{} \left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (b +a \sin \left (y\right )^{2}\right ) y^{\prime \prime }+a {y^{\prime }}^{2} \cos \left (y\right ) \sin \left (y\right )+A y \left (c +a \sin \left (y\right )^{2}\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} h \left (y\right ) y^{\prime \prime }+a h \left (y\right ) {y^{\prime }}^{2}+j \left (y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2} = 0
\]
|
✗ |
✗ |
✗ |
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| \[
{} \left (x y^{\prime }-y\right ) y^{\prime \prime }+4 {y^{\prime }}^{2} = 0
\]
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✓ |
✓ |
✗ |
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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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✗ |
✓ |
✗ |
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| \[
{} a \,x^{3} y^{\prime } y^{\prime \prime }+b y^{2} = 0
\]
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✗ |
✓ |
✗ |
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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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✗ |
✗ |
✗ |
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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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✓ |
✓ |
✗ |
|
| \[
{} \left (a \sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }\right ) y^{\prime \prime }-{y^{\prime }}^{2}-1 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} {y^{\prime \prime }}^{2}-a y-b = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} a^{2} {y^{\prime \prime }}^{2}-2 a x y^{\prime \prime }+y^{\prime } = 0
\]
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✗ |
✓ |
✗ |
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| \[
{} 2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2}-x \left (x +4 y^{\prime }\right ) y^{\prime \prime }+2 \left (x +y^{\prime }\right ) y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 4 {y^{\prime }}^{2}-2 \left (3 x y^{\prime }+y\right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (2-9 x \right ) x^{2} {y^{\prime \prime }}^{2}-6 \left (1-6 x \right ) x y^{\prime } y^{\prime \prime }+6 y y^{\prime \prime }-36 x {y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x} = 0
\]
|
✗ |
✗ |
✗ |
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| \[
{} \left (a^{2} y^{2}-b^{2}\right ) {y^{\prime \prime }}^{2}-2 a^{2} y {y^{\prime }}^{2} y^{\prime \prime }+\left (a^{2} {y^{\prime }}^{2}-1\right ) {y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2}-4 x y \left (x y^{\prime }-y\right )^{3} = 0
\]
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✓ |
✗ |
✗ |
|
| \[
{} 32 y^{\prime \prime } \left (x y^{\prime \prime }-y^{\prime }\right )^{3}+\left (2 y y^{\prime \prime }-{y^{\prime }}^{2}\right )^{3} = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} \sqrt {a {y^{\prime \prime }}^{2}+b {y^{\prime }}^{2}}+c y y^{\prime \prime }+d {y^{\prime }}^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime \prime }-a^{2} \left ({y^{\prime }}^{5}+2 {y^{\prime }}^{3}+y^{\prime }\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime \prime }+y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0
\]
|
✗ |
✗ |
✗ |
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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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✗ |
✗ |
✗ |
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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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| \[
{} y^{3} y^{\prime }-y^{\prime } y^{\prime \prime }+y y^{\prime \prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 15 {y^{\prime }}^{3}-18 y y^{\prime } y^{\prime \prime }+4 y^{2} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 40 {y^{\prime }}^{3}-45 y y^{\prime } y^{\prime \prime }+9 y^{2} y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }-3 y^{\prime } {y^{\prime \prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }-\left (a +3 y^{\prime }\right ) {y^{\prime \prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } y^{\prime \prime \prime }-a \sqrt {1+b^{2} {y^{\prime \prime }}^{2}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } y^{\prime \prime \prime \prime }-y^{\prime \prime } y^{\prime \prime \prime }+{y^{\prime }}^{3} y^{\prime \prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 3 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 9 {y^{\prime \prime }}^{2} y^{\left (5\right )}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+40 y^{\prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-f \left (y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime \prime } = f \left (y\right )
\]
|
✗ |
✗ |
✗ |
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| \[
{} [x^{\prime }\left (t \right ) = a x \left (t \right ), y^{\prime }\left (t \right ) = b]
\]
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✓ |
✓ |
✓ |
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| \[
{} [x^{\prime }\left (t \right ) = a y \left (t \right ), y^{\prime }\left (t \right ) = -a x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
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| \[
{} [x^{\prime }\left (t \right ) = a y \left (t \right ), y^{\prime }\left (t \right ) = b x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = a x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+a y \left (t \right )]
\]
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✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = a x \left (t \right )+b y \left (t \right ), y^{\prime }\left (t \right ) = c x \left (t \right )+b y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [a x^{\prime }\left (t \right )+b y^{\prime }\left (t \right ) = \alpha x \left (t \right )+\beta y \left (t \right ), b x^{\prime }\left (t \right )-a y^{\prime }\left (t \right ) = \beta x \left (t \right )-\alpha y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \{x^{\prime }\left (t \right )+3 x \left (t \right )+4 y \left (t \right ) = 0, y^{\prime }\left (t \right )+2 x \left (t \right )+5 y \left (t \right ) = 0\}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \{x^{\prime }\left (t \right ) = -5 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-7 y \left (t \right )\}
\]
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✓ |
✓ |
✓ |
|
| \[
{} \{x^{\prime }\left (t \right ) = a_{1} x \left (t \right )+b_{1} y \left (t \right )+c_{1}, y^{\prime }\left (t \right ) = a_{2} x \left (t \right )+b_{2} y \left (t \right )+c_{2}\}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \{x^{\prime }\left (t \right )+2 y \left (t \right ) = 3 t, y^{\prime }\left (t \right )-2 x \left (t \right ) = 4\}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right )+y \left (t \right )-t^{2}+6 t +1 = 0, -x \left (t \right )+y^{\prime }\left (t \right ) = -3 t^{2}+3 t +1]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right )+3 x \left (t \right )-y \left (t \right ) = {\mathrm e}^{2 t}, y^{\prime }\left (t \right )+x \left (t \right )+5 y \left (t \right ) = {\mathrm e}^{t}]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )+y \left (t \right ) = {\mathrm e}^{2 t}+t, x^{\prime }\left (t \right )-x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right ) = {\mathrm e}^{t}-1]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-y \left (t \right ) = {\mathrm e}^{t}, 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right ) = \cos \left (t \right )]
\]
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✓ |
✓ |
✓ |
|
| \[
{} [4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+2 x \left (t \right )+31 y \left (t \right ) = {\mathrm e}^{t}, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+x \left (t \right )+24 y \left (t \right ) = 3]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+11 x \left (t \right )+31 y \left (t \right ) = {\mathrm e}^{t}, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+8 x \left (t \right )+24 y \left (t \right ) = {\mathrm e}^{2 t}]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+44 x \left (t \right )+49 y \left (t \right ) = t, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+34 x \left (t \right )+38 y \left (t \right ) = {\mathrm e}^{t}]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ) f \left (t \right )+y \left (t \right ) g \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right ) g \left (t \right )+f \left (t \right ) y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right )+\left (a x \left (t \right )+b y \left (t \right )\right ) f \left (t \right ) = g \left (t \right ), y^{\prime }\left (t \right )+\left (c x \left (t \right )+d y \left (t \right )\right ) f \left (t \right ) = h \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = \cos \left (t \right ) x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right ) {\mathrm e}^{-\sin \left (t \right )}]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [t x^{\prime }\left (t \right )+y \left (t \right ) = 0, t y^{\prime }\left (t \right )+x \left (t \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|