| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=1-\operatorname {Heaviside}\left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.093 |
|
| \begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=k \left (\operatorname {Heaviside}\left (t -\frac {3}{2}\right )-\operatorname {Heaviside}\left (t -\frac {5}{2}\right )\right ) \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
8.302 |
|
| \begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\frac {\operatorname {Heaviside}\left (t -\frac {3}{2}\right )}{2}-\frac {\operatorname {Heaviside}\left (t -\frac {5}{2}\right )}{2} \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.013 |
|
| \begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )-\operatorname {Heaviside}\left (t -5-k \right ) \left (t -5-k \right )}{k} \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.410 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\delta \left (t -5\right )+\operatorname {Heaviside}\left (t -10\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.106 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+3 y&=\sin \left (t \right )+\delta \left (t -3 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.269 |
|
| \begin{align*}
y^{\prime \prime }+y&=\delta \left (t -2 \pi \right ) \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=2 \delta \left (t -\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.495 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.233 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.204 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.216 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{4}+y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.194 |
|
| \begin{align*}
y^{\prime \prime }+y&=\frac {\operatorname {Heaviside}\left (t -4+k \right )-\operatorname {Heaviside}\left (t -4-k \right )}{2 k} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.958 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
y^{\prime }&=2 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.162 |
|
| \begin{align*}
x y^{\prime }+y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.029 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.424 |
|
| \begin{align*}
2 y^{\prime }+x \left (y^{2}-1\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.840 |
|
| \begin{align*}
y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.237 |
|
| \begin{align*}
y^{\prime }&=-x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| \begin{align*}
y^{\prime }&=-x \sin \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
y^{\prime }&=x \ln \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
y^{\prime }&=-x \,{\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
y^{\prime }&=x \sin \left (x^{2}\right ) \\
y \left (\frac {\sqrt {2}\, \sqrt {\pi }}{2}\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| \begin{align*}
y^{\prime }&=\tan \left (x \right ) \\
y \left (\frac {\pi }{4}\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.996 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )-y \tan \left (x \right ) \\
y \left (\frac {\pi }{4}\right ) &= \frac {\pi \sqrt {2}}{8} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.704 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}-2 x^{2} y+2}{x^{3}} \\
y \left (1\right ) &= {\frac {3}{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.196 |
|
| \begin{align*}
y^{\prime }&=x \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.647 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (y+1\right )}{x} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.891 |
|
| \begin{align*}
y^{\prime }&=a y^{\frac {a -1}{a}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.210 |
|
| \begin{align*}
y^{\prime }&={| y|}+1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
3.978 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}-1+\frac {\sqrt {x^{2}+4 x +4 y}}{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
4.161 |
|
| \begin{align*}
y^{\prime }+a y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.049 |
|
| \begin{align*}
y^{\prime }+3 x^{2} y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.783 |
|
| \begin{align*}
x y^{\prime }+y \ln \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.453 |
|
| \begin{align*}
x y^{\prime }+3 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.420 |
|
| \begin{align*}
x^{2} y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.839 |
|
| \begin{align*}
y^{\prime }+\frac {\left (x +1\right ) y}{x}&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.440 |
|
| \begin{align*}
x y^{\prime }+\left (1+\frac {1}{\ln \left (x \right )}\right ) y&=0 \\
y \left ({\mathrm e}\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.700 |
|
| \begin{align*}
x y^{\prime }+\left (1+x \cot \left (x \right )\right ) y&=0 \\
y \left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.272 |
|
| \begin{align*}
y^{\prime }-\frac {2 x y}{x^{2}+1}&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.694 |
|
| \begin{align*}
y^{\prime }+\frac {k y}{x}&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.047 |
|
| \begin{align*}
y^{\prime }+\tan \left (k x \right ) y&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.428 |
|
| \begin{align*}
y^{\prime }+3 y&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.823 |
|
| \begin{align*}
y^{\prime }+\left (\frac {1}{x}-1\right ) y&=-\frac {2}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.335 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \,{\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.664 |
|
| \begin{align*}
y^{\prime }+\frac {2 x y}{x^{2}+1}&=\frac {{\mathrm e}^{-x^{2}}}{x^{2}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.178 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\frac {7}{x^{2}}+3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.926 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{x -1}&=\frac {1}{\left (x -1\right )^{5}}+\frac {\sin \left (x \right )}{\left (x -1\right )^{4}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.323 |
|
| \begin{align*}
x y^{\prime }+\left (2 x^{2}+1\right ) y&=x^{3} {\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.067 |
|
| \begin{align*}
x y^{\prime }+2 y&=\frac {2}{x^{2}}+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.094 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.171 |
|
| \begin{align*}
2 y+\left (x +1\right ) y^{\prime }&=\frac {\sin \left (x \right )}{x +1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.099 |
|
| \begin{align*}
\left (x -2\right ) \left (x -1\right ) y^{\prime }-\left (4 x -3\right ) y&=\left (x -2\right )^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.583 |
|
| \begin{align*}
y^{\prime }+2 \sin \left (x \right ) \cos \left (x \right ) y&={\mathrm e}^{-\sin \left (x \right )^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.850 |
|
| \begin{align*}
x^{2} y^{\prime }+3 y x&={\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.031 |
|
| \begin{align*}
y^{\prime }+7 y&={\mathrm e}^{3 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.088 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+4 y x&=\frac {2}{x^{2}+1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.020 |
|
| \begin{align*}
x y^{\prime }+3 y&=\frac {2}{x \left (x^{2}+1\right )} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.233 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=\cos \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.767 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\frac {2}{x^{2}}+1 \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.267 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime }+3 y&=\frac {1}{\left (x -1\right )^{3}}+\frac {\sin \left (x \right )}{\left (x -1\right )^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.652 |
|
| \begin{align*}
x y^{\prime }+2 y&=8 x^{2} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.669 |
|
| \begin{align*}
x y^{\prime }-2 y&=-x^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.455 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.583 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime }+3 y&=\frac {1+\left (x -1\right ) \sec \left (x \right )^{2}}{\left (x -1\right )^{3}} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.865 |
|
| \begin{align*}
\left (x +2\right ) y^{\prime }+4 y&=\frac {2 x^{2}+1}{x \left (x +2\right )^{3}} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.658 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }-2 y x&=x \left (x^{2}-1\right ) \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.927 |
|
| \begin{align*}
x y^{\prime }-2 y&=-1 \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.168 |
|
| \begin{align*}
\sec \left (y\right )^{2} y^{\prime }-3 \tan \left (y\right )&=-1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.557 |
|
| \begin{align*}
{\mathrm e}^{y^{2}} \left (2 y y^{\prime }+\frac {2}{x}\right )&=\frac {1}{x^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.168 |
|
| \begin{align*}
\frac {x y^{\prime }}{y}+2 \ln \left (y\right )&=4 x^{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.384 |
|
| \begin{align*}
\frac {y^{\prime }}{\left (y+1\right )^{2}}-\frac {1}{x \left (y+1\right )}&=-\frac {3}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.819 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x^{2}+2 x +1}{-2+y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.747 |
|
| \begin{align*}
\sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.409 |
|
| \begin{align*}
x y^{\prime }+y^{2}+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.396 |
|
| \begin{align*}
\left (3 y^{3}+3 y \cos \left (y\right )+1\right ) y^{\prime }+\frac {\left (2 x +1\right ) y}{x^{2}+1}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.944 |
|
| \begin{align*}
x^{2} y y^{\prime }&=\left (y^{2}-1\right )^{{3}/{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.206 |
|
| \begin{align*}
y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.198 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.542 |
|
| \begin{align*}
y^{\prime }&=\left (x -1\right ) \left (-1+y\right ) \left (-2+y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.507 |
|
| \begin{align*}
\left (-1+y\right )^{2} y^{\prime }&=2 x +3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.944 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+3 x +2}{-2+y} \\
y \left (1\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.615 |
|
| \begin{align*}
y^{\prime }+x \left (y^{2}+y\right )&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.167 |
|
| \begin{align*}
\left (3 y^{2}+4 y\right ) y^{\prime }+2 x +\cos \left (x \right )&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.628 |
|
| \begin{align*}
y^{\prime }+\frac {\left (y+1\right ) \left (-1+y\right ) \left (-2+y\right )}{x +1}&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
3.658 |
|
| \begin{align*}
y^{\prime }+2 x \left (y+1\right )&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.598 |
|
| \begin{align*}
y^{\prime }&=2 x y \left (1+y^{2}\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
7.596 |
|
| \begin{align*}
y^{\prime } \left (x^{2}+2\right )&=4 x \left (y^{2}+2 y+1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.357 |
|
| \begin{align*}
y^{\prime }&=-2 x \left (y^{3}-3 y+2\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.504 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{1+2 y} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.404 |
|
| \begin{align*}
y^{\prime }&=2 y-y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.337 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
y \left (3\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.565 |
|
| \begin{align*}
y^{\prime }+x^{2} \left (y+1\right ) \left (-2+y\right )^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.773 |
|
| \begin{align*}
\left (x +1\right ) \left (x -2\right ) y^{\prime }+y&=0 \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.161 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.433 |
|