|
# |
ODE |
Mathematica |
Maple |
Sympy |
|
\[
{} \left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }-3 x y^{2}+x = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (a y^{2}+2 b x y+c \,x^{2}\right ) y^{\prime }+b y^{2}+2 c x y+d \,x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (b \left (\beta y+\alpha x \right )^{2}-\beta \left (a x +b y\right )\right ) y^{\prime }+a \left (\beta y+\alpha x \right )^{2}-\alpha \left (a x +b y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (a y+b x +c \right )^{2} y^{\prime }+\left (\alpha y+\beta x +\gamma \right )^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x \left (y^{2}-3 x \right ) y^{\prime }+2 y^{3}-5 x y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x \left (y^{2}+x^{2}-a \right ) y^{\prime }-\left (a +x^{2}+y^{2}\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x \left (y^{2}+x^{2} y+x^{2}\right ) y^{\prime }-2 y^{3}-2 x^{2} y^{2}+x^{4} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (3 x y^{2}-x^{2}\right ) y^{\prime }+y^{3}-2 x y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (y^{3}-3 x \right ) y^{\prime }-3 y+x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (a +x^{2}+y^{2}\right ) y y^{\prime }+\left (y^{2}+x^{2}-a \right ) x = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (\frac {y^{2}}{b}+\frac {x^{2}}{a}\right ) \left (y y^{\prime }+x \right )+\frac {\left (a -b \right ) \left (y y^{\prime }-x \right )}{a +b} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (2 a y^{3}+3 a x y^{2}-b \,x^{3}+c \,x^{2}\right ) y^{\prime }-a y^{3}+c y^{2}+3 b \,x^{2} y+2 b \,x^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (2 x y^{3}+x y+x^{2}\right ) y^{\prime }-x y+y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (3 x y^{3}-4 x y+y\right ) y^{\prime }+y^{2} \left (y^{2}-2\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (7 x y^{3}+y-5 x \right ) y^{\prime }+y^{4}-5 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (a x y^{3}+c \right ) x y^{\prime }+\left (b \,x^{3} y+c \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (2 y^{3} x^{3}-x \right ) y^{\prime }+2 y^{3} x^{3}-y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y \left (\left (b x +a y\right )^{3}+b \,x^{3}\right ) y^{\prime }+x \left (\left (b x +a y\right )^{3}+a y^{3}\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x +2 y+2 x^{2} y^{3}+y^{4} x \right ) y^{\prime }+y^{5}+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} a \,x^{2} y^{n} y^{\prime }-2 x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{m} x^{n} \left (a x y^{\prime }+b y\right )+\alpha x y^{\prime }+\beta y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (2 x^{{5}/{2}} y^{{3}/{2}}+x^{2} y-x \right ) y^{\prime }-x^{{3}/{2}} y^{{5}/{2}}+x y^{2}-y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (\sqrt {1+y^{2}}+a x \right ) y^{\prime }+\sqrt {x^{2}+1}+a y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (y \sqrt {x^{2}+y^{2}}+\left (y^{2}-x^{2}\right ) \sin \left (\alpha \right )-2 x y \cos \left (\alpha \right )\right ) y^{\prime }+x \sqrt {x^{2}+y^{2}}+2 x y \sin \left (\alpha \right )+\left (y^{2}-x^{2}\right ) \cos \left (\alpha \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x \sqrt {1+x^{2}+y^{2}}-y \left (x^{2}+y^{2}\right )\right ) y^{\prime }-y \sqrt {1+x^{2}+y^{2}}-x \left (x^{2}+y^{2}\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (\frac {\operatorname {e1} \left (x +a \right )}{\left (\left (x +a \right )^{2}+y^{2}\right )^{{3}/{2}}}+\frac {\operatorname {e2} \left (x -a \right )}{\left (\left (x -a \right )^{2}+y^{2}\right )^{{3}/{2}}}\right ) y^{\prime }-y \left (\frac {\operatorname {e1}}{\left (\left (x +a \right )^{2}+y^{2}\right )^{{3}/{2}}}+\frac {\operatorname {e2}}{\left (\left (x -a \right )^{2}+y^{2}\right )^{{3}/{2}}}\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left ({\mathrm e}^{x}+x \,{\mathrm e}^{y}\right ) y^{\prime }+y \,{\mathrm e}^{x}+{\mathrm e}^{y} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x \left (y \ln \left (x y\right )+y-a x \right ) y^{\prime }-y \left (a x \ln \left (x y\right )-y+a x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \sin \left (y\right )+\cos \left (x \right ) y+\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime } \cot \left (\frac {y}{x}\right )+2 x \sin \left (\frac {y}{x}\right )-y \cot \left (\frac {y}{x}\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } \left (\cos \left (y\right )-\sin \left (\alpha \right ) \sin \left (x \right )\right ) \cos \left (y\right )+\left (\cos \left (x \right )-\sin \left (\alpha \right ) \sin \left (y\right )\right ) \cos \left (x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x \cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }-y \sin \left (x \right )+\sin \left (y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2} \cos \left (y\right )+2 y \sin \left (x \right )\right ) y^{\prime }+2 x \sin \left (y\right )+y^{2} \cos \left (x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } \cos \left (a y\right )-b \left (1-c \cos \left (a y\right )\right ) \sqrt {\cos \left (a y\right )^{2}-1+c \cos \left (a y\right )} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x \sin \left (x y\right )+\cos \left (x +y\right )-\sin \left (y\right )\right ) y^{\prime }+y \sin \left (x y\right )+\cos \left (x +y\right )+\cos \left (x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x y^{\prime }-y\right ) \cos \left (\frac {y}{x}\right )^{2}+x = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }-\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (y f \left (x^{2}+y^{2}\right )-x \right ) y^{\prime }+y+x f \left (x^{2}+y^{2}\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} f \left (x^{2}+a y^{2}\right ) \left (a y y^{\prime }+x \right )-y-x y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2}+a y+b \,x^{2} = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2}+a x y^{\prime }+b y+c \,x^{2} = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} {y^{\prime }}^{2}-2 y^{\prime } x^{2}+2 x y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2}+\left (y^{\prime }-y\right ) {\mathrm e}^{x} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2}-2 y y^{\prime }-2 x = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2}-\left (4 y+1\right ) y^{\prime }+\left (4 y+1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2}+a y y^{\prime }-b x -c = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2}-x y y^{\prime }+y^{2} \ln \left (a y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 {y^{\prime }}^{2}-2 y^{\prime } x^{2}+3 x y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 3 {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} a {y^{\prime }}^{2}+b \,x^{2} y^{\prime }+c x y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} a {y^{\prime }}^{2}+y y^{\prime }-x = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} a {y^{\prime }}^{2}-y y^{\prime }-x = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2} x -2 y^{\prime }-y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2} x +4 y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2} x +y y^{\prime }+a = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2} x +y y^{\prime }-x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2} x +y y^{\prime }+x^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2} x -y y^{\prime }+a = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2} x -y y^{\prime }+a y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2} x -2 y y^{\prime }+a = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (1+x \right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (3 x +1\right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9 = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (5+3 x \right ) {y^{\prime }}^{2}-\left (3 y+x \right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} a x {y^{\prime }}^{2}+\left (b x -a y+c \right ) y^{\prime }-b y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} a x {y^{\prime }}^{2}-\left (a y+b x -a -b \right ) y^{\prime }+b y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (\operatorname {a2} x +\operatorname {c2} \right ) {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {a0} x +\operatorname {b0} y+\operatorname {c0} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x y^{\prime }+a \right )^{2}-2 a y+x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x y^{\prime }+y+2 x \right )^{2}-4 x y-4 x^{2}-4 a = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{4}+\left (-x^{2}+1\right ) y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-1 = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+a \right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}+b = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (x^{2}+2 x y+y^{2}+2\right ) y^{\prime }+2 y^{2}+1 = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x \left (x^{2}-1\right ) {y^{\prime }}^{2}+2 \left (-x^{2}+1\right ) y y^{\prime }+x y^{2}-x = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {\mathrm e}^{-2 x} {y^{\prime }}^{2}-\left (y^{\prime }-1\right )^{2}+{\mathrm e}^{-2 y} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left ({y^{\prime }}^{2}+y^{2}\right ) \cos \left (x \right )^{4}-a^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (y-2 x \right ) {y^{\prime }}^{2}-2 \left (x -1\right ) y^{\prime }+y-2 = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 y {y^{\prime }}^{2}-\left (4 x -5\right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 4 y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (b_{2} y+a_{2} x +c_{2} \right ) {y^{\prime }}^{2}+\left (a_{1} x +b_{1} y+c_{1} \right ) y^{\prime }+a_{0} x +b_{0} y+c_{0} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (a y-x^{2}\right ) {y^{\prime }}^{2}+2 x y {y^{\prime }}^{2}-y^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x y {y^{\prime }}^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-x y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (2 x y-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+2 x y-y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} a x y {y^{\prime }}^{2}-\left (a y^{2}+b \,x^{2}+c \right ) y^{\prime }+b x y = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 a x +y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+a y^{2}+b x +c = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+a -x^{2}+2 y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (a -1\right ) b +a \,x^{2}+\left (1-a \right ) y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|