|
# |
ODE |
Mathematica |
Maple |
Sympy |
|
\[
{} y^{\prime }-f \left (x \right ) \left (y-g \left (x \right )\right ) \sqrt {\left (y-a \right ) \left (y-b \right )} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime }+f \left (x \right ) \cos \left (a y\right )+g \left (x \right ) \sin \left (a y\right )+h \left (x \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime }-a \left (1+\tan \left (y\right )^{2}\right )+\tan \left (y\right ) \tan \left (x \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x y^{\prime }-\sin \left (x -y\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y y^{\prime }+x^{3}+y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y y^{\prime }+a y+\frac {\left (a^{2}-1\right ) x}{4}+b \,x^{n} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y y^{\prime }+a y+b \,{\mathrm e}^{x}-2 a = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x y y^{\prime }-y^{2}+x y+x^{3}-2 x^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x \left (a +y\right ) y^{\prime }+b y+c x = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (B x y+A \,x^{2}+a x +b y+c \right ) y^{\prime }-B g \left (x \right )^{2}+A x y+\alpha x +\beta y+\gamma = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x^{2} y-1\right ) y^{\prime }+8 x y^{2}-8 = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x^{n \left (n +1\right )} y-1\right ) y^{\prime }+2 \left (n +1\right )^{2} x^{n -1} \left (x^{n^{2}} y^{2}-1\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (\frac {\operatorname {e1} \left (x +a \right )}{\left (\left (x +a \right )^{2}+y^{2}\right )^{{3}/{2}}}+\frac {\operatorname {e2} \left (x -a \right )}{\left (\left (x -a \right )^{2}+y^{2}\right )^{{3}/{2}}}\right ) y^{\prime }-y \left (\frac {\operatorname {e1}}{\left (\left (x +a \right )^{2}+y^{2}\right )^{{3}/{2}}}+\frac {\operatorname {e2}}{\left (\left (x -a \right )^{2}+y^{2}\right )^{{3}/{2}}}\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (\operatorname {a2} x +\operatorname {c2} \right ) {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {a0} x +\operatorname {b0} y+\operatorname {c0} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left ({y^{\prime }}^{2}+y^{2}\right ) \cos \left (x \right )^{4}-a^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (a y-x^{2}\right ) {y^{\prime }}^{2}+2 x y {y^{\prime }}^{2}-y^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x y {y^{\prime }}^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-x y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (\operatorname {b2} y+\operatorname {a2} x +\operatorname {c2} \right )^{2} {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {b0} y+\operatorname {a0} +\operatorname {c0} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} \left (x y^{2}-1\right ) {y^{\prime }}^{2}+2 x^{2} y^{2} \left (y-x \right ) y^{\prime }-y^{2} \left (x^{2} y-1\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} \left (x^{2} y^{4}-1\right ) {y^{\prime }}^{2}+2 x^{3} y^{3} \left (y^{2}-x^{2}\right ) y^{\prime }-y^{2} \left (x^{4} y^{2}-1\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} {y^{\prime }}^{2}-\left (x^{2}+x y^{2}+y^{4}\right ) {y^{\prime }}^{2}+\left (x y^{6}+x^{2} y^{4}+x^{3} y^{2}\right ) y^{\prime }-x^{3} y^{6} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = -\frac {1}{-\left (y^{3}\right )^{{2}/{3}} x -\textit {\_F1} \left (y^{3}-3 \ln \left (x \right )\right ) \left (y^{3}\right )^{{1}/{3}} x}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = -\frac {i \left (32 i x +64+64 y^{4}+32 x^{2} y^{2}+4 x^{4}+64 y^{6}+48 x^{2} y^{4}+12 x^{4} y^{2}+x^{6}\right )}{128 y}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = -\frac {i \left (i x +1+x^{4}+2 x^{2} y^{2}+y^{4}+x^{6}+3 x^{4} y^{2}+3 x^{2} y^{4}+y^{6}\right )}{y}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }-\left (a^{2} x^{2 n}-1\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }-\left (4 a^{2} b^{2} x^{2} {\mathrm e}^{2 b \,x^{2}}-1\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+2 a y^{\prime }+f \left (x \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+a y^{\prime }-x y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+a \,x^{2} y^{\prime }+f \left (x \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+\left (a \,x^{2}+b \right ) x y^{\prime }+f \left (x \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+f \left (x \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+f \left (x \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{3} y^{\prime \prime }+y^{\prime } x^{2}+\left (a \,x^{2}+b x +a \right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-2 x^{3} y^{\prime }-\left (\left (a -n \right ) \left (a +n +1\right ) x^{2} \left (x^{2}-1\right )+2 a \,x^{2}+n \left (n +1\right ) \left (x^{2}-1\right )\right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime } = -\frac {\left (\left (1-4 a \right ) x^{2}-1\right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (\left (-v^{2}+x^{2}\right ) \left (x^{2}-1\right )^{2}+4 a \left (a +1\right ) x^{4}-2 a \,x^{2} \left (x^{2}-1\right )\right ) y}{x^{2} \left (x^{2}-1\right )^{2}}
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime } = -\frac {\left (x^{2} \left (\left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right )+\left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )+\left (x^{2}-\operatorname {a3} \right ) \left (x^{2}-\operatorname {a1} \right )\right )-\left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )\right ) y^{\prime }}{x \left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )}-\frac {\left (A \,x^{2}+B \right ) y}{x \left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime } = -\frac {\left (x^{2} \sin \left (x \right )-2 x \cos \left (x \right )\right ) y^{\prime }}{x^{2} \cos \left (x \right )}-\frac {\left (2 \cos \left (x \right )-x \sin \left (x \right )\right ) y}{x^{2} \cos \left (x \right )}
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime } = -\frac {b \cos \left (x \right ) y^{\prime }}{\sin \left (x \right ) a}-\frac {\left (c \cos \left (x \right )^{2}+d \cos \left (x \right )+e \right ) y}{a \sin \left (x \right )^{2}}
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime } = -\frac {f^{\prime }\left (x \right ) y^{\prime }}{2 f \left (x \right )}-\frac {g \left (x \right ) y}{f \left (x \right )}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime \prime }-\left (6 k^{2} \sin \left (x \right )^{2}+a \right ) y^{\prime }+b y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime \prime }+2 f \left (x \right ) y^{\prime }+f^{\prime }\left (x \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} 2 x y^{\prime \prime \prime }+3 \left (2 a x +k \right ) y^{\prime \prime }+6 \left (a k +b x \right ) y^{\prime }+\left (3 b k +2 c x \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime \prime }+\left (1+x \right ) y^{\prime \prime }-y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime \prime }-\left (x +\nu \right ) x y^{\prime \prime }+\nu \left (2 x +1\right ) y^{\prime }-\nu \left (1+x \right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} x^{3} y^{\prime \prime \prime }+3 \left (1-a \right ) x^{2} y^{\prime \prime }+\left (4 b^{2} c^{2} x^{2 c +1}+1-4 \nu ^{2} c^{2}+3 a \left (a -1\right ) x \right ) y^{\prime }+\left (4 b^{2} c^{2} \left (c -a \right ) x^{2 c}+a \left (4 \nu ^{2} c^{2}-a^{2}\right )\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{3} y^{\prime \prime \prime }+x^{2} \left (x +3\right ) y^{\prime \prime }+5 \left (x -6\right ) x y^{\prime }+\left (4 x +30\right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime \prime \prime }+a \left (b x -1\right ) y^{\prime \prime }+a b y^{\prime }+\lambda y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime \prime \prime }+\left (a \,x^{2}+\lambda b +c \right ) y^{\prime \prime }+\left (a \,x^{2}+\beta \lambda +\gamma \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime \prime \prime }+2 x y^{\prime \prime \prime }+a y-b \,x^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}-1\right )^{2} y^{\prime \prime \prime \prime }+10 x \left (x^{2}-1\right ) y^{\prime \prime \prime }+\left (24 x^{2}-8-2 \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )\right ) \left (x^{2}-1\right )\right ) y^{\prime \prime }-6 x \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )-2\right ) y^{\prime }+\left (\left (\mu \left (\mu +1\right )-\nu \left (\nu +1\right )\right )^{2}-2 \mu \left (\mu +1\right )-2 \nu \left (\nu +1\right )\right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} y^{\left (5\right )}-a x y-b = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x y^{\left (5\right )}-\left (a A_{1} -A_{0} \right ) x -A_{1} -\left (\left (a A_{2} -A_{1} \right ) x +A_{2} \right ) y^{\prime } = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x -a \right )^{5} \left (x -b \right )^{5} y^{\left (5\right )}-c y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }-6 y^{2}-x = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+a y^{2}+b x +c = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }-2 y^{3}-x y+a = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }-2 a^{2} y^{3}+2 a b x y-b = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+d +b x y+c y+a y^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+a \,x^{r} y^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }-\frac {1}{\left (a y^{2}+b x y+c \,x^{2}+\alpha y+\beta x +\gamma \right )^{{3}/{2}}} = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+a \,{\mathrm e}^{x} \sqrt {y} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+{\mathrm e}^{x} \sin \left (y\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta \sin \left (x \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta f \left (x \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }-3 y^{\prime }-y^{2}-2 y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }-7 y^{\prime }-y^{{3}/{2}}+12 y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }-\frac {\left (3 n +4\right ) y^{\prime }}{n}-\frac {2 \left (n +1\right ) \left (n +2\right ) y \left (y^{\frac {n}{n +1}}-1\right )}{n^{2}} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+a y^{\prime }+b y^{n}+\frac {\left (a^{2}-1\right ) y}{4} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{y}-2 a = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+a y^{\prime }+f \left (x \right ) \sin \left (y\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+\left (y+3 f \left (x \right )\right ) y^{\prime }-y^{3}+f \left (x \right ) y^{2}+y \left (f^{\prime }\left (x \right )+2 f \left (x \right )^{2}\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+a {y^{\prime }}^{2}+b y^{\prime }+c y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b \sin \left (y\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x y^{\prime \prime }+2 y^{\prime }-x y^{n} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x y^{\prime \prime }+2 y^{\prime }+a \,x^{v} y^{n} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x y^{\prime \prime }+2 y^{\prime }+x \,{\mathrm e}^{y} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x y^{\prime \prime }+a y^{\prime }+b x \,{\mathrm e}^{y} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x y^{\prime \prime }+a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime } = a \left (y^{n}-y\right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+a \left ({\mathrm e}^{y}-1\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+a y {y^{\prime }}^{2}+b x = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }-\sqrt {a \,x^{2} {y^{\prime }}^{2}+b y^{2}} = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} 4 x^{2} y^{\prime \prime }-x^{4} {y^{\prime }}^{2}+4 y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} 2 x^{3} y^{\prime \prime }+x^{2} \left (9+2 x y\right ) y^{\prime }+b +x y \left (a +3 x y-2 x^{2} y^{2}\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} 2 \left (-x^{k}+4 x^{3}\right ) \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )-\left (k \,x^{k -1}-12 x^{2}\right ) \left (3 y^{\prime }+y^{2}\right )+a x y+b = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{4} y^{\prime \prime }+a^{2} y^{n} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \sqrt {x}\, y^{\prime \prime }-y^{{3}/{2}} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y y^{\prime \prime }-a x = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y y^{\prime \prime }-a \,x^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+a y y^{\prime }-2 a y^{2}+b y^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+\left (-1+a y\right ) y^{\prime }-y \left (1+y\right ) \left (b^{2} y^{2}-a^{2}\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+f \left (x \right ) y^{2}+a = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}-4 \left (2 y+x \right ) y^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+1+2 x y^{2}+a y^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+\left (b x +a y\right ) y^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+b -4 \left (x^{2}+a \right ) y^{2}-8 x y^{3}-3 y^{4} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2}+f \left (x \right ) y^{2} = 0
\]
|
✗ |
✗ |
✗ |
|