| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=-\left (-\frac {\ln \left (y\right )}{x}+\frac {\ln \left (y\right )}{x \ln \left (x \right )}-\textit {\_F1} \left (x \right )\right ) y \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
12.371 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{y^{2}+y^{{3}/{2}}+\sqrt {y}\, x^{2}-2 y^{{3}/{2}} x +y^{{5}/{2}}+x^{3}-3 x^{2} y+3 x y^{2}-y^{3}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
13.092 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{-2 \left (x -y\right ) \left (x +y\right )}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{-2 \left (x -y\right ) \left (x +y\right )}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
13.036 |
|
| \begin{align*}
y^{\prime }&=-\frac {\left (-\frac {\ln \left (y\right )^{2}}{2 x}-\textit {\_F1} \left (x \right )\right ) y}{\ln \left (y\right )} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✓ |
✓ |
9.035 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{2 \left (x -y\right )^{2} \left (x +y\right )^{2}}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{2 \left (x -y\right )^{2} \left (x +y\right )^{2}}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
13.406 |
|
| \begin{align*}
y^{\prime }&=\frac {-8 x^{2} y^{3}+16 x y^{2}+16 x y^{3}-8+12 y x -6 y^{2} x^{2}+x^{3} y^{3}}{16 \left (-2+y x -2 y\right ) x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
29.424 |
|
| \begin{align*}
y^{\prime }&=-\frac {x \left ({\mathrm e}^{-3 x^{2}} x^{6}-6 \,{\mathrm e}^{-2 x^{2}} x^{4} y+12 x^{2} {\mathrm e}^{-x^{2}} y^{2}-2 \,{\mathrm e}^{-2 x^{2}} x^{4}+8 x^{2} {\mathrm e}^{-x^{2}} y+8 x^{2} {\mathrm e}^{-x^{2}}-8 y^{3}-8 y^{2}-8 \,{\mathrm e}^{-x^{2}}-8\right )}{8} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
15.841 |
|
| \begin{align*}
y^{\prime }&=\frac {\left ({\mathrm e}^{-\frac {y}{x}} y x +{\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x^{2}+{\mathrm e}^{-\frac {y}{x}} x +x \right ) {\mathrm e}^{\frac {y}{x}}}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
20.801 |
|
| \begin{align*}
y^{\prime }&=-\frac {16 x y^{3}-8 y^{3}-8 y+8 x y^{2}-2 x^{2} y^{3}-8+12 y x -6 y^{2} x^{2}+x^{3} y^{3}}{32 y x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
8.174 |
|
| \begin{align*}
y^{\prime }&=\frac {\left ({\mathrm e}^{-\frac {y}{x}} y x +{\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x^{2}+{\mathrm e}^{-\frac {y}{x}} x +x^{4}\right ) {\mathrm e}^{\frac {y}{x}}}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
8.415 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x^{2} y-2 x^{3}-2 x -x y^{2}-y+x^{3} y^{3}+3 y^{2} x^{4}+3 x^{5} y+x^{6}}{x \left (x^{2}+y x +1\right )} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.196 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (27 y^{3}+27 \,{\mathrm e}^{3 x^{2}} y+18 \,{\mathrm e}^{3 x^{2}} y^{2}+3 y^{3} {\mathrm e}^{3 x^{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y+9 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y^{2}+{\mathrm e}^{\frac {9 x^{2}}{2}} y^{3}\right ) {\mathrm e}^{3 x^{2}} x \,{\mathrm e}^{-\frac {9 x^{2}}{2}}}{243 y} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
15.452 |
|
| \begin{align*}
y^{\prime }&=-\frac {-x^{2}-y x -x^{3}-x y^{2}+2 y \ln \left (x \right ) x^{2}-x^{3} \ln \left (x \right )^{2}-y^{3}+3 x y^{2} \ln \left (x \right )-3 x^{2} \ln \left (x \right )^{2} y+x^{3} \ln \left (x \right )^{3}}{x^{2}} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
2.793 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{2}+1+y^{2}+\frac {x^{2} y}{4}-y x -\frac {x^{4}}{8}+\frac {x^{3}}{8}+\frac {x^{2}}{4}+y^{3}-\frac {3 y^{2} x^{2}}{4}-\frac {3 x y^{2}}{2}+\frac {3 x^{4} y}{16}+\frac {3 x^{3} y}{4}-\frac {x^{6}}{64}-\frac {3 x^{5}}{32} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
4.271 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+1+y^{2}+\frac {7 x^{2} y}{2}-2 y x +\frac {13 x^{4}}{16}-\frac {3 x^{3}}{2}+x^{2}+y^{3}+\frac {3 y^{2} x^{2}}{4}-3 x y^{2}+\frac {3 x^{4} y}{16}-\frac {3 x^{3} y}{2}+\frac {x^{6}}{64}-\frac {3 x^{5}}{16} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✓ |
7.610 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{4}+1+y^{2}+\frac {7 x^{2} y}{16}-\frac {y x}{2}+\frac {5 x^{4}}{128}-\frac {5 x^{3}}{64}+\frac {x^{2}}{16}+y^{3}+\frac {3 y^{2} x^{2}}{8}-\frac {3 x y^{2}}{4}+\frac {3 x^{4} y}{64}-\frac {3 x^{3} y}{16}+\frac {x^{6}}{512}-\frac {3 x^{5}}{256} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
4.433 |
|
| \begin{align*}
y^{\prime }&=\frac {-2 y-2 \ln \left (2 x +1\right )-2+2 x y^{3}+y^{3}+6 y^{2} \ln \left (2 x +1\right ) x +3 y^{2} \ln \left (2 x +1\right )+6 y \ln \left (2 x +1\right )^{2} x +3 y \ln \left (2 x +1\right )^{2}+2 \ln \left (2 x +1\right )^{3} x +\ln \left (2 x +1\right )^{3}}{\left (2 x +1\right ) \left (y+\ln \left (2 x +1\right )+1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
36.770 |
|
| \begin{align*}
y^{\prime }&=\frac {-x^{2}+x +1+y^{2}+5 x^{2} y-2 y x +4 x^{4}-3 x^{3}+y^{3}+3 y^{2} x^{2}-3 x y^{2}+3 x^{4} y-6 x^{3} y+x^{6}-3 x^{5}}{x} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
4.704 |
|
| \begin{align*}
y^{\prime }&=\frac {-32 y x +16 x^{3}+16 x^{2}-32 x -64 y^{3}+48 y^{2} x^{2}+96 x y^{2}-12 x^{4} y-48 x^{3} y-48 x^{2} y+x^{6}+6 x^{5}+12 x^{4}}{-64 y+16 x^{2}+32 x -64} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
8.174 |
|
| \begin{align*}
y^{\prime }&=\frac {x y \ln \left (x \right )+x^{2} \ln \left (x \right )-2 y x -x^{2}-y^{2}-y^{3}+3 x y^{2} \ln \left (x \right )-3 x^{2} \ln \left (x \right )^{2} y+x^{3} \ln \left (x \right )^{3}}{x \left (-y+x \ln \left (x \right )-x \right )} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.334 |
|
| \begin{align*}
y^{\prime }&=\frac {-32 y x -72 x^{3}+32 x^{2}-32 x +64 y^{3}+48 y^{2} x^{2}-192 x y^{2}+12 x^{4} y-96 x^{3} y+192 x^{2} y+x^{6}-12 x^{5}+48 x^{4}}{64 y+16 x^{2}-64 x +64} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
8.046 |
|
| \begin{align*}
y^{\prime }&=-\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{\frac {2 \left (x -y\right )^{3} \left (x +y\right )^{3}}{-y^{2}+x^{2}-1}}}{-y^{2}-2 y x -x^{2}+{\mathrm e}^{\frac {2 \left (x -y\right )^{3} \left (x +y\right )^{3}}{-y^{2}+x^{2}-1}}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
14.638 |
|
| \begin{align*}
y^{\prime }&=\frac {-128 y x -24 x^{3}+32 x^{2}-128 x +512 y^{3}+192 y^{2} x^{2}-384 x y^{2}+24 x^{4} y-96 x^{3} y+96 x^{2} y+x^{6}-6 x^{5}+12 x^{4}}{512 y+64 x^{2}-128 x +512} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
7.649 |
|
| \begin{align*}
y^{\prime }&=\frac {-32 a x y-8 a^{2} x^{3}-16 b \,x^{2} a -32 a x +64 y^{3}+48 a \,x^{2} y^{2}+96 b x y^{2}+12 a^{2} x^{4} y+48 y a \,x^{3} b +48 b^{2} x^{2} y+a^{3} x^{6}+6 a^{2} x^{5} b +12 b^{2} x^{4} a +8 b^{3} x^{3}}{64 y+16 a \,x^{2}+32 b x +64} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
8.222 |
|
| \begin{align*}
y^{\prime }&=\frac {-32 y x -8 x^{3}-16 a \,x^{2}-32 x +64 y^{3}+48 y^{2} x^{2}+96 a x y^{2}+12 x^{4} y+48 y a \,x^{3}+48 y a^{2} x^{2}+x^{6}+6 x^{5} a +12 a^{2} x^{4}+8 a^{3} x^{3}}{64 y+16 x^{2}+32 a x +64} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
7.757 |
|
| \begin{align*}
y^{\prime }&=\frac {\left ({\mathrm e}^{-3 x^{2}} x^{6}-6 \,{\mathrm e}^{-2 x^{2}} x^{4} y+12 x^{2} {\mathrm e}^{-x^{2}} y^{2}-4 \,{\mathrm e}^{-2 x^{2}} x^{4}+8 x^{2} {\mathrm e}^{-x^{2}} y+8 x^{2} {\mathrm e}^{-x^{2}}+4 x^{2} {\mathrm e}^{-2 x^{2}}-8 y^{3}-8 y \,{\mathrm e}^{-x^{2}}-8 \,{\mathrm e}^{-x^{2}}\right ) x}{-8 y+4 x^{2} {\mathrm e}^{-x^{2}}-8} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
11.339 |
|
| \begin{align*}
y^{\prime }&=\frac {2 \cos \left (x \right ) x^{2}+2 x^{3} \sin \left (x \right )-2 x \sin \left (x \right )+2 x +2 y^{2} x^{2}-4 x \sin \left (x \right ) y+4 y \cos \left (x \right ) x^{2}+4 y x +3-\cos \left (2 x \right )-2 \sin \left (2 x \right ) x -4 \sin \left (x \right )+x^{2} \cos \left (2 x \right )+x^{2}+4 \cos \left (x \right ) x}{2 x^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
10.097 |
|
| \begin{align*}
y^{\prime }&=-\frac {216 y}{-216 y^{4}-252 y^{3}-396 y^{2}-216 y+36 x^{2}-72 y x +60 y^{5}-36 x y^{3}-72 x y^{2}-24 y^{4} x +4 y^{8}+12 y^{7}+33 y^{6}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
8.152 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2} y+x^{4}+2 x^{3}-3 x^{2}+y x +x +y^{3}+3 y^{2} x^{2}-3 x y^{2}+3 x^{4} y-6 x^{3} y+x^{6}-3 x^{5}}{x \left (y+x^{2}-x +1\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
8.427 |
|
| \begin{align*}
y^{\prime }&=-\frac {a x}{2}+1+y^{2}+\frac {a \,x^{2} y}{2}+b x y+\frac {a^{2} x^{4}}{16}+\frac {a \,x^{3} b}{4}+\frac {b^{2} x^{2}}{4}+y^{3}+\frac {3 a \,x^{2} y^{2}}{4}+\frac {3 b x y^{2}}{2}+\frac {3 a^{2} x^{4} y}{16}+\frac {3 y a \,x^{3} b}{4}+\frac {3 b^{2} x^{2} y}{4}+\frac {a^{3} x^{6}}{64}+\frac {3 a^{2} x^{5} b}{32}+\frac {3 b^{2} x^{4} a}{16}+\frac {b^{3} x^{3}}{8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
4.141 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+1+y^{2}+\frac {x^{2} y}{2}+a x y+\frac {x^{4}}{16}+\frac {a \,x^{3}}{4}+\frac {a^{2} x^{2}}{4}+y^{3}+\frac {3 y^{2} x^{2}}{4}+\frac {3 a x y^{2}}{2}+\frac {3 x^{4} y}{16}+\frac {3 y a \,x^{3}}{4}+\frac {3 y a^{2} x^{2}}{4}+\frac {x^{6}}{64}+\frac {3 x^{5} a}{32}+\frac {3 a^{2} x^{4}}{16}+\frac {a^{3} x^{3}}{8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
4.123 |
|
| \begin{align*}
y^{\prime }&=-\frac {-y+x^{2} \sqrt {x^{2}+y^{2}}-x \sqrt {x^{2}+y^{2}}\, y+x^{4} \sqrt {x^{2}+y^{2}}-x^{3} \sqrt {x^{2}+y^{2}}\, y+x^{5} \sqrt {x^{2}+y^{2}}-x^{4} \sqrt {x^{2}+y^{2}}\, y}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
19.999 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (\ln \left (x \right )+\ln \left (y\right )-1+x \ln \left (x \right )^{2}+2 x \ln \left (y\right ) \ln \left (x \right )+x \ln \left (y\right )^{2}+x^{3} \ln \left (x \right )^{2}+2 x^{3} \ln \left (y\right ) \ln \left (x \right )+x^{3} \ln \left (y\right )^{2}+x^{4} \ln \left (x \right )^{2}+2 x^{4} \ln \left (y\right ) \ln \left (x \right )+x^{4} \ln \left (y\right )^{2}\right )}{x} \\
\end{align*} |
[NONE] |
✗ |
✓ |
✓ |
✗ |
11.077 |
|
| \begin{align*}
y^{\prime }&=\frac {150 x^{3}+125 \sqrt {x}+125+125 y^{2}-100 x^{3} y-500 \sqrt {x}\, y+20 x^{6}+200 x^{{7}/{2}}+500 x +125 y^{3}-150 x^{3} y^{2}-750 y^{2} \sqrt {x}+60 x^{6} y+600 y x^{{7}/{2}}+1500 y x -8 x^{9}-120 x^{{13}/{2}}-600 x^{4}-1000 x^{{3}/{2}}}{125 x} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
9.765 |
|
| \begin{align*}
y^{\prime }&=\frac {-150 x^{3} y+60 x^{6}+350 x^{{7}/{2}}-150 x^{3}-125 \sqrt {x}\, y+250 x -125 \sqrt {x}-125 y^{3}+150 x^{3} y^{2}+750 y^{2} \sqrt {x}-60 x^{6} y-600 y x^{{7}/{2}}-1500 y x +8 x^{9}+120 x^{{13}/{2}}+600 x^{4}+1000 x^{{3}/{2}}}{25 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
15.820 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-1-x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2}-x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} \ln \left (x \right )+x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y+2 x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y \ln \left (x \right )+x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y \ln \left (x \right )^{2}\right )}{\left (1+\ln \left (x \right )\right ) x} \\
\end{align*} |
[_Bernoulli] |
✗ |
✓ |
✓ |
✓ |
13.234 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-1-x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}}-x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} \ln \left (x \right )+x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y+2 x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y \ln \left (x \right )+x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y \ln \left (x \right )^{2}\right )}{\left (1+\ln \left (x \right )\right ) x} \\
\end{align*} |
[_Bernoulli] |
✗ |
✓ |
✓ |
✓ |
13.035 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +4 y \ln \left (2 x +1\right ) x +6 y^{2} \ln \left (2 x +1\right ) x +6 y \ln \left (2 x +1\right )^{2} x +2 \ln \left (2 x +1\right )^{3} x +2 x y^{3}+2 \ln \left (2 x +1\right )^{2} x +2 x y^{2}-1+3 y^{2} \ln \left (2 x +1\right )+3 y \ln \left (2 x +1\right )^{2}+y^{2}+y^{3}+2 y \ln \left (2 x +1\right )+\ln \left (2 x +1\right )^{2}+\ln \left (2 x +1\right )^{3}}{2 x +1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
3.847 |
|
| \begin{align*}
y^{\prime }&=\frac {-y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{3} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x} \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
7.529 |
|
| \begin{align*}
y^{\prime }&=\frac {-y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{2} \sin \left (\frac {y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x} \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
4.607 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{2+2 y^{4}-4 y^{2} x^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 y^{2} x^{4}-2 x^{6}}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{2+2 y^{4}-4 y^{2} x^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 y^{2} x^{4}-2 x^{6}}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.994 |
|
| \begin{align*}
y^{\prime }&=\frac {4 x \left (-1+a \right ) \left (1+a \right ) \left (-y^{2}+a^{2} x^{2}-x^{2}-2\right )}{-4 y^{3}+4 y a^{2} x^{2}-4 x^{2} y-8 y-a^{2} y^{6}+3 a^{4} y^{4} x^{2}-6 y^{4} a^{2} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-9 y^{2} a^{2} x^{4}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}-4 a^{2} x^{6}+y^{6}+3 x^{2} y^{4}+3 y^{2} x^{4}+x^{6}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.571 |
|
| \begin{align*}
y^{\prime }&=\frac {-4 \cos \left (x \right ) x +4 x^{2} \sin \left (x \right )+4 x +4+4 y^{2}+8 y \cos \left (x \right ) x -8 y x +2 x^{2} \cos \left (2 x \right )+6 x^{2}-8 \cos \left (x \right ) x^{2}+4 y^{3}+12 y^{2} \cos \left (x \right ) x -12 x y^{2}+6 y x^{2} \cos \left (2 x \right )+18 x^{2} y-24 y \cos \left (x \right ) x^{2}+x^{3} \cos \left (3 x \right )+15 \cos \left (x \right ) x^{3}-6 x^{3} \cos \left (2 x \right )-10 x^{3}}{4 x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
10.744 |
|
| \begin{align*}
y^{\prime }&=-\frac {8 x \left (-1+a \right ) \left (1+a \right )}{8+x^{6}-8 y+2 x^{4}-a^{2} y^{6}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}-8 y^{2} a^{2} x^{2}+2 y^{4}+3 x^{2} y^{4}-2 y^{4} a^{2}-6 a^{2} x^{4}-8 a^{2}+4 y^{2} x^{2}+y^{6}+3 y^{2} x^{4}+3 a^{4} y^{4} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-9 y^{2} a^{2} x^{4}+4 a^{4} y^{2} x^{2}-4 a^{2} x^{6}-6 y^{4} a^{2} x^{2}-2 a^{6} x^{4}+6 a^{4} x^{4}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
4.142 |
|
| \begin{align*}
y^{\prime }&=\frac {-y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +2 \sin \left (\frac {y}{x}\right ) x^{3} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{4} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x} \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
8.283 |
|
| \begin{align*}
y^{\prime }&=-\frac {1296 y}{216-2376 y^{2}+216 x^{2}+216 x^{3}-1728 y^{3}+1080 x y^{3}-1296 y+594 x y^{6}-324 x^{2} y^{3}-432 y x -1944 y^{4}-216 x^{2} y^{4}-846 y^{7}-648 y^{2} x^{2}-612 y^{5}-882 y^{6}+216 x y^{2}-648 x^{2} y-570 y^{8}+1080 x y^{5}+1152 y^{4} x -126 y^{10}-8 y^{12}-36 y^{11}+72 y^{8} x +216 y^{7} x -315 y^{9}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
8.985 |
|
| \begin{align*}
y^{\prime }&=-\frac {x \left (-513-432 x -456 x^{6}-540 y^{2}-1134 x^{2}-756 x^{3}-216 y^{3}-378 y-864 x^{4}-144 x^{7}+864 x^{5} y^{2}-648 y^{3} x^{4}-648 x^{2} y^{3}+288 x^{7} y+720 x^{3} y+432 x^{3} y^{2}+1008 x^{5} y-288 x^{6} y-576 x^{5}-1296 y^{2} x^{2}-216 x^{4} y-594 x^{2} y-96 x^{8}-972 y^{2} x^{4}+432 y^{2} x^{7}+64 x^{9}-216 x^{6} y^{2}-288 y x^{8}-216 x^{6} y^{3}\right )}{216 \left (x^{2}+1\right )^{4}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
4.708 |
|
| \begin{align*}
y^{\prime }&=\frac {-\sin \left (\frac {y}{x}\right ) y x -y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right ) x +y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{4} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x \left (x +1\right )} \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
8.776 |
|
| \begin{align*}
y^{\prime }&=\frac {y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right ) x +y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )-\sin \left (\frac {y}{x}\right ) y x -y \sin \left (\frac {y}{x}\right )+2 \sin \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x}{2 \cos \left (\frac {y}{x}\right ) \sin \left (\frac {y}{2 x}\right ) x \cos \left (\frac {y}{2 x}\right ) \left (x +1\right )} \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
11.381 |
|
| \begin{align*}
y^{\prime }&=-\frac {216 y \left (-2 y^{4}-3 y^{3}-6 y^{2}-6 y+6 x +6\right )}{-1296 y^{2}+216 x^{3}+1728 y^{3}-648 x y^{3}-1296 y+594 x y^{6}-324 x^{2} y^{3}-1296 y x +2808 y^{4}-216 x^{2} y^{4}+594 y^{7}-648 y^{2} x^{2}+4428 y^{5}+2484 y^{6}-1944 x y^{2}-648 x^{2} y-18 y^{8}+1080 x y^{5}-432 y^{4} x -126 y^{10}-8 y^{12}-36 y^{11}+72 y^{8} x +216 y^{7} x -315 y^{9}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
10.309 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (y x +1\right )^{3}}{x^{5}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
8.418 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (-x^{2}+2 x^{2} y-2 x^{4}+1\right )}{-x^{2}+y} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.461 |
|
| \begin{align*}
y^{\prime }&=y \left (y^{2}+y \,{\mathrm e}^{b x}+{\mathrm e}^{2 b x}\right ) {\mathrm e}^{-2 b x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✓ |
3.511 |
|
| \begin{align*}
y^{\prime }&=y^{3}-3 y^{2} x^{2}+3 x^{4} y-x^{6}+2 x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✓ |
2.040 |
|
| \begin{align*}
y^{\prime }&=y^{3}+y^{2} x^{2}+\frac {x^{4} y}{3}+\frac {x^{6}}{27}-\frac {2 x}{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✓ |
2.085 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (y^{2} x^{7}+x^{4} y+x -3\right )}{x} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✓ |
✓ |
6.585 |
|
| \begin{align*}
y^{\prime }&=y \left (y^{2}+y \,{\mathrm e}^{-x^{2}}+{\mathrm e}^{-2 x^{2}}\right ) {\mathrm e}^{2 x^{2}} x \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
10.334 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (y^{2}+y x +x^{2}+x \right )}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
3.686 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x}{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Abel] |
✓ |
✓ |
✓ |
✓ |
3.059 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3} y^{3}+6 y^{2} x^{2}+12 y x +8+2 x}{x^{3}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
3.207 |
|
| \begin{align*}
y^{\prime }&=\frac {a^{3} x^{3} y^{3}+3 y^{2} a^{2} x^{2}+3 a x y+1+a^{2} x}{x^{3} a^{3}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
3.690 |
|
| \begin{align*}
y^{\prime }&=\frac {y \,{\mathrm e}^{-\frac {x^{2}}{2}} \left (2 y^{2}+2 y \,{\mathrm e}^{\frac {x^{2}}{4}}+2 \,{\mathrm e}^{\frac {x^{2}}{2}}+x \,{\mathrm e}^{\frac {x^{2}}{2}}\right )}{2} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
45.014 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x^{2}}{\left (x -1\right ) \left (x +1\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
8.467 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (y^{2} x^{2}+y x \,{\mathrm e}^{x}+{\mathrm e}^{2 x}\right ) {\mathrm e}^{-2 x} \left (x -1\right )}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _Abel] |
✗ |
✓ |
✓ |
✗ |
15.217 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (y x +1\right ) \left (y^{2} x^{2}+x^{2} y+2 y x +1+x +x^{2}\right )}{x^{5}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
3.637 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3}-3 x y^{2} \ln \left (x \right )+3 x^{2} \ln \left (x \right )^{2} y-x^{3} \ln \left (x \right )^{3}+x^{2}+y x}{x^{2}} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
2.394 |
|
| \begin{align*}
y^{\prime }&=-F \left (x \right ) \left (-a \,x^{2}+y^{2}\right )+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
2.949 |
|
| \begin{align*}
y^{\prime }&=-F \left (x \right ) \left (y^{2}-2 y x -x^{2}\right )+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
3.599 |
|
| \begin{align*}
y^{\prime }&=-F \left (x \right ) \left (-a y^{2}-b \,x^{2}\right )+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
3.349 |
|
| \begin{align*}
y^{\prime }&=-F \left (x \right ) \left (-y^{2}+2 x^{2} y+1-x^{4}\right )+2 x \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
11.174 |
|
| \begin{align*}
y^{\prime }&=-F \left (x \right ) \left (x^{2}+2 y x -y^{2}\right )+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
3.617 |
|
| \begin{align*}
y^{\prime }&=-F \left (x \right ) \left (-7 x y^{2}-x^{3}\right )+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
2.947 |
|
| \begin{align*}
y^{\prime }&=-F \left (x \right ) \left (-y^{2}-2 y \ln \left (x \right )-\ln \left (x \right )^{2}\right )+\frac {y}{x \ln \left (x \right )} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
13.586 |
|
| \begin{align*}
y^{\prime }&=-x^{3} \left (-y^{2}-2 y \ln \left (x \right )-\ln \left (x \right )^{2}\right )+\frac {y}{x \ln \left (x \right )} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
5.408 |
|
| \begin{align*}
y^{\prime }&=\left (y-{\mathrm e}^{x}\right )^{2}+{\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
23.755 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (y-\operatorname {Si}\left (x \right )\right )^{2}+\sin \left (x \right )}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
7.456 |
|
| \begin{align*}
y^{\prime }&=\left (\cos \left (x \right )+y\right )^{2}+\sin \left (x \right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (y-\ln \left (x \right )-\operatorname {Ci}\left (x \right )\right )^{2}+\cos \left (x \right )}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
63.691 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (y-x +\ln \left (x +1\right )\right )^{2}+x}{x +1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.242 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x^{2} y+x^{3}+x y \ln \left (x \right )-y^{2}-y x}{x^{2} \left (\ln \left (x \right )+x \right )} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
4.244 |
|
| \begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.860 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.649 |
|
| \begin{align*}
y^{\prime \prime }+y-\sin \left (x n \right )&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.914 |
|
| \begin{align*}
y^{\prime \prime }+y-a \cos \left (b x \right )&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.816 |
|
| \begin{align*}
y^{\prime \prime }+y-\sin \left (a x \right ) \sin \left (b x \right )&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.410 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.182 |
|
| \begin{align*}
y^{\prime \prime }-2 y-4 x^{2} {\mathrm e}^{x^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
29.042 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} y-\cot \left (a x \right )&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
34.393 |
|
| \begin{align*}
y^{\prime \prime }+l y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.527 |
|
| \begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \begin{align*}
y^{\prime \prime }-\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.272 |
|
| \begin{align*}
y^{\prime \prime }-\left (x^{2}+a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
1.734 |
|
| \begin{align*}
y^{\prime \prime }-\left (a^{2} x^{2}+a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.381 |
|
| \begin{align*}
y^{\prime \prime }-c \,x^{a} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.914 |
|
| \begin{align*}
y^{\prime \prime }-\left (a^{2} x^{2 n}-1\right ) y&=0 \\
\end{align*} |
[_Titchmarsh] |
✗ |
✗ |
✗ |
✗ |
1.120 |
|
| \begin{align*}
y^{\prime \prime }+\left (a \,x^{2 c}+b \,x^{c -1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
1.525 |
|
| \begin{align*}
y^{\prime \prime }+\left ({\mathrm e}^{2 x}-v^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.041 |
|
| \begin{align*}
a \,{\mathrm e}^{b x} y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.878 |
|
| \begin{align*}
y^{\prime \prime }-\left (4 a^{2} b^{2} x^{2} {\mathrm e}^{2 b \,x^{2}}-1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
1.595 |
|
| \begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{2 x}+b \,{\mathrm e}^{x}+c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
1.446 |
|