|
# |
ODE |
Mathematica |
Maple |
Sympy |
|
\[
{} y^{\prime }-\frac {y-x^{2} \sqrt {-y^{2}+x^{2}}}{x y \sqrt {-y^{2}+x^{2}}+x} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }-\sqrt {\frac {a y^{2}+b y+c}{a \,x^{2}+b x +c}} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }-\sqrt {\frac {a y^{4}+b y^{2}+1}{a \,x^{4}+b \,x^{2}+1}} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }-\sqrt {\left (b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0} \right ) \left (a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0} \right )} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }-\sqrt {\frac {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}{b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }-\sqrt {\frac {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}{a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }-\left (\frac {a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}{a_{3} y^{3}+a_{2} y^{2}+a_{1} y+a_{0}}\right )^{{2}/{3}} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }-f \left (x \right ) \left (y-g \left (x \right )\right ) \sqrt {\left (y-a \right ) \left (y-b \right )} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime }-a \cos \left (y\right )+b = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }+a \sin \left (\alpha y+\beta x \right )+b = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }+f \left (x \right ) \cos \left (a y\right )+g \left (x \right ) \sin \left (a y\right )+h \left (x \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime }+f \left (x \right ) \sin \left (y\right )+\left (1-f^{\prime }\left (x \right )\right ) \cos \left (y\right )-f^{\prime }\left (x \right )-1 = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }+2 \tan \left (y\right ) \tan \left (x \right )-1 = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }-a \left (1+\tan \left (y\right )^{2}\right )+\tan \left (y\right ) \tan \left (x \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime }-\tan \left (x y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }-x^{a -1} y^{1-b} f \left (\frac {x^{a}}{a}+\frac {y^{b}}{b}\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }-\frac {y-x f \left (x^{2}+a y^{2}\right )}{x +a y f \left (x^{2}+a y^{2}\right )} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 y^{\prime }-3 y^{2}-4 a y-b -c \,{\mathrm e}^{-2 a x} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }+x^{2}+y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }+a y^{2}-y+b \,x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }+a y^{2}-b y+c \,x^{2 b} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }+a y^{2}-b y-c \,x^{\beta } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }+a +x y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }+x y^{2}-y-a \,x^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }+a x y^{2}+2 y+b x = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }+a x y^{2}+b y+c x +d = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }+x^{a} y^{2}+\frac {\left (a -b \right ) y}{2}+x^{b} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }+a \,x^{\alpha } y^{2}+b y-c \,x^{\beta } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }+f \left (x \right ) \left (y^{2}-x^{2}\right )-y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }+y^{3}+3 x y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }+a \sqrt {x^{2}+y^{2}}-y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }-x \sqrt {x^{2}+y^{2}}-y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }-x \left (y-x \right ) \sqrt {x^{2}+y^{2}}-y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }-{\mathrm e}^{\frac {y}{x}} x -y-x = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }-y \left (x \ln \left (\frac {x^{2}}{y}\right )+2\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }-\sin \left (x -y\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x y^{\prime }+\left (\sin \left (y\right )-3 x^{2} \cos \left (y\right )\right ) \cos \left (y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }-y f \left (x^{a} y^{b}\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }+a y-f \left (x \right ) g \left (x^{a} y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} \left (y^{\prime }+y^{2}\right )+a \,x^{k}-b \left (b -1\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} \left (y^{\prime }-y^{2}\right )-a \,x^{2} y+a x +2 = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} \left (y^{\prime }+a y^{2}\right )+b \,x^{\alpha }+c = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } x^{2}+a y^{3}-a \,x^{2} y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } x^{2}+x y^{3}+a y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } x^{2}+a \,x^{2} y^{3}+b y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+1\right ) y^{\prime }+\left (1+y^{2}\right ) \left (2 x y-1\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right )-x \left (x^{2}+1\right ) \cos \left (y\right )^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}-1\right ) y^{\prime }+a \left (1-2 x y+y^{2}\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 y^{\prime } x^{2}-2 y^{2}-x y+2 a^{2} x = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 y^{\prime } x^{2}-2 y^{2}-3 x y+2 a^{2} x = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 x \left (x -1\right ) y^{\prime }+\left (x -1\right ) y^{2}-x = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 3 \left (x^{2}-4\right ) y^{\prime }+y^{2}-x y-3 = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (a x +b \right )^{2} y^{\prime }+\left (a x +b \right ) y^{3}+c y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x \left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right ) y^{2}-x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 3 x \left (x^{2}-1\right ) y^{\prime }+x y^{2}-\left (x^{2}+1\right ) y-3 x = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (a \,x^{2}+b x +c \right ) \left (x y^{\prime }-y\right )-y^{2}+x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{n} y^{\prime }+y^{2}-\left (n -1\right ) x^{n -1} y+x^{2 n -2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{n} y^{\prime }-a y^{2}-b \,x^{2 n -2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2 n +1} y^{\prime }-a y^{3}-b \,x^{3 n} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{m \left (n -1\right )+n} y^{\prime }-a y^{n}-b \,x^{n \left (1+m \right )} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x \ln \left (x \right ) y^{\prime }-y^{2} \ln \left (x \right )-\left (2 \ln \left (x \right )^{2}+1\right ) y-\ln \left (x \right )^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \sin \left (x \right ) y^{\prime }-y^{2} \sin \left (x \right )^{2}+\left (\cos \left (x \right )-3 \sin \left (x \right )\right ) y+4 = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \sin \left (x \right ) \cos \left (x \right ) y^{\prime }-y-\sin \left (x \right )^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (a \sin \left (x \right )^{2}+b \right ) y^{\prime }+a y \sin \left (2 x \right )+A x \left (a \sin \left (x \right )^{2}+c \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 f \left (x \right ) y^{\prime }+2 f \left (x \right ) y^{2}-f^{\prime }\left (x \right ) y-2 f \left (x \right )^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y y^{\prime }+x^{3}+y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y y^{\prime }+a y+x = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y y^{\prime }+a y+\frac {\left (a^{2}-1\right ) x}{4}+b \,x^{n} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y y^{\prime }+a y+b \,{\mathrm e}^{x}-2 a = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y y^{\prime }+x +f \left (x^{2}+y^{2}\right ) g \left (x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (1+y\right ) y^{\prime }-y-x = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (4 y+11 x -11\right ) y^{\prime }-25 y-8 x +62 = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (a y+b x +c \right ) y^{\prime }+\alpha y+\beta x +\gamma = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y y^{\prime }-y^{2}+x y+x^{3}-2 x^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x \left (4+y\right ) y^{\prime }-y^{2}-2 y-2 x = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x \left (a +y\right ) y^{\prime }+b y+c x = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x \left (x +2 y-1\right ) y^{\prime }-\left (2 x +y+1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y \left (2 x -y-1\right )+x \left (2 y-x -1\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (2 x y+4 x^{3}\right ) y^{\prime }+y^{2}+112 x^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (3 x +2\right ) \left (y-2 x -1\right ) y^{\prime }-y^{2}+x y-7 x^{2}-9 x -3 = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (3+6 x y+x^{2}\right ) y^{\prime }+2 x +2 x y+3 y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (a x y+b \,x^{n}\right ) y^{\prime }+\alpha y^{3}+\beta y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (B x y+A \,x^{2}+a x +b y+c \right ) y^{\prime }-B g \left (x \right )^{2}+A x y+\alpha x +\beta y+\gamma = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x^{2} y-1\right ) y^{\prime }+x y^{2}-1 = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2} y-1\right ) y^{\prime }-x y^{2}+1 = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2} y-1\right ) y^{\prime }+8 x y^{2}-8 = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x \left (x y+x^{4}-1\right ) y^{\prime }-y \left (x y-x^{4}-1\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{n \left (n +1\right )} y-1\right ) y^{\prime }+2 \left (n +1\right )^{2} x^{n -1} \left (x^{n^{2}} y^{2}-1\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (y-x \right ) \sqrt {x^{2}+1}\, y^{\prime }-a \sqrt {\left (1+y^{2}\right )^{3}} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (-x +y^{2}\right ) y^{\prime }-y+x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (y+2 x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 x y+x^{2}+b +\left (a +x^{2}+y^{2}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+y^{2}+x \right ) y^{\prime }-y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x +2 y+y^{2}\right ) y^{\prime }+y \left (1+y\right )+\left (x +y\right )^{2} y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (y+3 x -1\right )^{2} y^{\prime }-\left (2 y-1\right ) \left (4 y+6 x -3\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 3 \left (y^{2}-x^{2}\right ) y^{\prime }+2 y^{3}-6 x y \left (1+x \right )-3 \,{\mathrm e}^{x} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (3 x^{2}+2 x y+4 y^{2}\right ) y^{\prime }+2 x^{2}+6 x y+y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (1-3 x +2 y\right )^{2} y^{\prime }-\left (3 y-2 x -4\right )^{2} = 0
\]
|
✓ |
✓ |
✗ |
|