| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }+9 y&=\sin \left (x \right )^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 t x_{1}^{2} \\
x_{2}^{\prime }&=\frac {x_{2}+t}{t} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.036 |
|
| \begin{align*}
x_{1}^{\prime }&={\mathrm e}^{t -x_{1}} \\
x_{2}^{\prime }&=2 \,{\mathrm e}^{x_{1}} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.036 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.032 |
|
| \begin{align*}
x_{1}^{\prime }&=\frac {x_{1}^{2}}{x_{2}} \\
x_{2}^{\prime }&=x_{2}-x_{1} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| \begin{align*}
x^{\prime }&=\frac {{\mathrm e}^{-x}}{t} \\
y^{\prime }&=\frac {x \,{\mathrm e}^{-y}}{t} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| \begin{align*}
x^{\prime }&=\frac {t +y}{x+y} \\
y^{\prime }&=\frac {-t +x}{x+y} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✗ |
✗ |
0.036 |
|
| \begin{align*}
x^{\prime }&=\frac {t -y}{-x+y} \\
y^{\prime }&=\frac {-t +x}{-x+y} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| \begin{align*}
x^{\prime }&=\frac {t +y}{x+y} \\
y^{\prime }&=\frac {t +x}{x+y} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✗ |
✗ |
0.031 |
|
| \begin{align*}
x^{\prime }&=-9 y \\
y^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
x^{\prime }&=t +y \\
y^{\prime }&=-t +x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \begin{align*}
x^{\prime }+3 x+4 y&=0 \\
y^{\prime }+2 x+5 y&=0 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 4 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
x^{\prime }&=x+5 y \\
y^{\prime }&=-x-3 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \begin{align*}
4 x^{\prime }-y^{\prime }+3 x&=\sin \left (t \right ) \\
x^{\prime }+y&=\cos \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.837 |
|
| \begin{align*}
x^{\prime }&=z-y \\
y^{\prime }&=z \\
z^{\prime }&=z-x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| \begin{align*}
x^{\prime }&=y+z \\
y^{\prime }&=x+z \\
z^{\prime }&=x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
x^{\prime \prime }&=y \\
y^{\prime \prime }&=x \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.024 |
|
| \begin{align*}
x^{\prime \prime }+y^{\prime }+x&=0 \\
x^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} | system_of_ODEs | ✗ | ✓ | ✓ | ✓ | 0.032 |
|
| \begin{align*}
x^{\prime \prime }&=3 x+y \\
y^{\prime }&=-2 x \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.028 |
|
| \begin{align*}
x^{\prime \prime }&=x^{2}+y \\
y^{\prime }&=-2 x x^{\prime }+x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✗ |
✗ |
0.020 |
|
| \begin{align*}
x^{\prime }&=x^{2}+y^{2} \\
y^{\prime }&=2 x y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.027 |
|
| \begin{align*}
x^{\prime }&=-\frac {1}{y} \\
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.026 |
|
| \begin{align*}
x^{\prime }&=\frac {x}{y} \\
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.026 |
|
| \begin{align*}
x^{\prime }&=\frac {y}{x-y} \\
y^{\prime }&=\frac {x}{x-y} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.029 |
|
| \begin{align*}
x^{\prime }&=\sin \left (x\right ) \cos \left (y\right ) \\
y^{\prime }&=\cos \left (x\right ) \sin \left (y\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.042 |
|
| \begin{align*}
{\mathrm e}^{t} x^{\prime }&=\frac {1}{y} \\
{\mathrm e}^{t} y^{\prime }&=\frac {1}{x} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.036 |
|
| \begin{align*}
x^{\prime }&=\cos \left (x\right )^{2} \cos \left (y\right )^{2}+\sin \left (x\right )^{2} \cos \left (y\right )^{2} \\
y^{\prime }&=-\frac {\sin \left (2 x\right ) \sin \left (2 y\right )}{2} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.046 |
|
| \begin{align*}
x^{\prime }&=8 y-x \\
y^{\prime }&=x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=-x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=x-3 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-2 x+4 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
x^{\prime }&=4 x-5 y \\
y^{\prime }&=x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| \begin{align*}
x^{\prime }&=y+z-x \\
y^{\prime }&=x-y+z \\
z^{\prime }&=x+y-z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| \begin{align*}
x^{\prime }&=2 x-y+z \\
y^{\prime }&=x+2 y-z \\
z^{\prime }&=x-y+2 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| \begin{align*}
x^{\prime }&=2 x-y+z \\
y^{\prime }&=x+z \\
z^{\prime }&=y-2 z-3 x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
x^{\prime }+2 x-y&=-{\mathrm e}^{2 t} \\
y^{\prime }+3 x-2 y&=6 \,{\mathrm e}^{2 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| \begin{align*}
x^{\prime }&=x+y-\cos \left (t \right ) \\
y^{\prime }&=-y-2 x+\cos \left (t \right )+\sin \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| \begin{align*}
x^{\prime }&=y+\tan \left (t \right )^{2}-1 \\
y^{\prime }&=\tan \left (t \right )-x \\
\end{align*} | system_of_ODEs | ✓ | ✓ | ✓ | ✓ | 0.878 |
|
| \begin{align*}
x^{\prime }&=-4 x-2 y+\frac {2}{{\mathrm e}^{t}-1} \\
y^{\prime }&=6 x+3 y-\frac {3}{{\mathrm e}^{t}-1} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.029 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+\frac {1}{\cos \left (t \right )} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=1-x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| \begin{align*}
x^{\prime }&=3-2 y \\
y^{\prime }&=2 x-2 t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.655 |
|
| \begin{align*}
x^{\prime }&=-y+\sin \left (t \right ) \\
y^{\prime }&=x+\cos \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| \begin{align*}
x^{\prime }&=x+y+{\mathrm e}^{t} \\
y^{\prime }&=x+y-{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| \begin{align*}
x^{\prime }&=4 x-5 y+4 t -1 \\
y^{\prime }&=x-2 y+t \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| \begin{align*}
x^{\prime }&=y-x+{\mathrm e}^{t} \\
y^{\prime }&=x-y+{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
x^{\prime }+y&=t^{2} \\
-x+y^{\prime }&=t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \begin{align*}
x^{\prime }+y^{\prime }+y&={\mathrm e}^{-t} \\
2 x^{\prime }+y^{\prime }+2 y&=\sin \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| \begin{align*}
x^{\prime }&=2 x+y-2 z+2-t \\
y^{\prime }&=1-x \\
z^{\prime }&=x+y-z+1-t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.326 |
|
| \begin{align*}
x^{\prime }+x+2 y&=2 \,{\mathrm e}^{-t} \\
y^{\prime }+y+z&=1 \\
z^{\prime }+z&=1 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.858 |
|
| \begin{align*}
x^{\prime }&=5 x+4 y \\
y^{\prime }&=x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \begin{align*}
x^{\prime }&=6 x+y \\
y^{\prime }&=4 x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
x^{\prime }&=2 x-4 y+1 \\
y^{\prime }&=-x+5 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| \begin{align*}
x^{\prime }&=3 x+y+{\mathrm e}^{t} \\
y^{\prime }&=x+3 y-{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| \begin{align*}
x^{\prime }&=2 x+4 y+\cos \left (t \right ) \\
y^{\prime }&=-x-2 y+\sin \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| \begin{align*}
x^{\prime }+3 x&={\mathrm e}^{-2 t} \\
x \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.182 |
|
| \begin{align*}
x^{\prime }-3 x&=3 t^{3}+3 t^{2}+2 t +1 \\
x \left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. | [[_linear, ‘class A‘]] | ✓ | ✓ | ✓ | ✓ | 0.152 |
|
| \begin{align*}
x^{\prime }-x&=\cos \left (t \right )-\sin \left (t \right ) \\
x \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.144 |
|
| \begin{align*}
2 x^{\prime }+6 x&=t \,{\mathrm e}^{-3 t} \\
x \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.128 |
|
| \begin{align*}
x^{\prime }+x&=2 \sin \left (t \right ) \\
x \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.161 |
|
| \begin{align*}
x^{\prime \prime }&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.099 |
|
| \begin{align*}
x^{\prime \prime }&=1 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.086 |
|
| \begin{align*}
x^{\prime \prime }&=\cos \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.144 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.079 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.099 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }&=1 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.116 |
|
| \begin{align*}
x^{\prime \prime }+x&=t \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.090 |
|
| \begin{align*}
x^{\prime \prime }+6 x^{\prime }&=12 t +2 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.102 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }+2 x&=2 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.097 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+4 x&=4 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -4 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.135 |
|
| \begin{align*}
2 x^{\prime \prime }-2 x^{\prime }&=\left (t +1\right ) {\mathrm e}^{t} \\
x \left (0\right ) &= {\frac {1}{2}} \\
x^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.146 |
|
| \begin{align*}
x^{\prime \prime }+x&=2 \cos \left (t \right ) \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.191 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{4}}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.487 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2} \left (x^{3}+1\right )}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.706 |
|
| \begin{align*}
y^{\prime }+y^{3} \sin \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.500 |
|
| \begin{align*}
y^{\prime }&=\frac {7 x^{2}-1}{7+5 y} \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 1.954 |
|
| \begin{align*}
y^{\prime }&=\sin \left (2 x \right )^{2} \cos \left (y\right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
3.108 |
|
| \begin{align*}
y^{\prime } x&=\sqrt {1-y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.562 |
|
| \begin{align*}
y^{\prime } y&=\left (x y^{2}+x \right ) {\mathrm e}^{x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.740 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+{\mathrm e}^{-x}}{y^{2}-{\mathrm e}^{y}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.647 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{1+y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.510 |
|
| \begin{align*}
y^{\prime }&=\frac {\sec \left (x \right )^{2}}{y^{3}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.264 |
|
| \begin{align*}
y^{\prime }&=4 \sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
9.221 |
|
| \begin{align*}
y^{\prime }&=x \left (y-y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.920 |
|
| \begin{align*}
y^{\prime }&=\left (1-12 x \right ) y^{2} \\
y \left (0\right ) &= -{\frac {1}{8}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.728 |
|
| \begin{align*}
y^{\prime }&=\frac {3-2 x}{y} \\
y \left (1\right ) &= -6 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.753 |
|
| \begin{align*}
x +y y^{\prime } {\mathrm e}^{-x}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.305 |
|
| \begin{align*}
r^{\prime }&=\frac {r^{2}}{\theta } \\
r \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.612 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x}{y+x^{2} y} \\
y \left (0\right ) &= -7 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.984 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{1+2 y} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.500 |
|
| \begin{align*}
y^{\prime }&=2 x y^{2}+4 x^{3} y^{2} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.707 |
|
| \begin{align*}
y^{\prime }&=x^{2} {\mathrm e}^{-3 y} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.505 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2}\right ) \tan \left (2 x \right ) \\
y \left (0\right ) &= -\sqrt {3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
5.576 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (x^{2}+1\right ) y^{5}}{6} \\
y \left (0\right ) &= -2^{{1}/{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.843 |
|
| \begin{align*}
y^{\prime }&=\frac {-{\mathrm e}^{x}+3 x^{2}}{2 y-11} \\
y \left (0\right ) &= 11 \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 2.634 |
|
| \begin{align*}
x^{2} y^{\prime }&=y-y x \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.801 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.501 |
|
| \begin{align*}
2 y^{\prime } y&=\frac {x}{\sqrt {x^{2}-4}} \\
y \left (3\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.024 |
|
| \begin{align*}
\sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime }&=0 \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
25.050 |
|
| \begin{align*}
\sqrt {-x^{2}+1}\, y^{2} y^{\prime }&=\arcsin \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.484 |
|