| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{\prime }&=y+z \\
y^{\prime }&=x+z \\
z^{\prime }&=x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.362 |
|
| \begin{align*}
x^{\prime }+x-5 y&=0 \\
y^{\prime }+4 x+5 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.179 |
|
| \begin{align*}
x^{\prime }+3 y^{\prime }+y&={\mathrm e}^{t} \\
-x+y^{\prime }&=y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.122 |
|
| \begin{align*}
x^{\prime }-3 x-6 y&=27 t^{2} \\
x^{\prime }+y^{\prime }-3 y&=5 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 5 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.110 |
|
| \begin{align*}
x^{\prime \prime }&=-2 y \\
y^{\prime }&=y-x^{\prime } \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 10 \\
y \left (0\right ) &= 5 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.053 |
|
| \begin{align*}
y^{\prime \prime }&=x-2 \\
x^{\prime \prime }&=y+2 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.044 |
|
| \begin{align*}
x^{\prime }+y^{\prime }&=\cos \left (t \right ) \\
x+y^{\prime \prime }&=2 \\
\end{align*}
With initial conditions \begin{align*}
x \left (\pi \right ) &= 2 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.044 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=x-y \\
z^{\prime }&=2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.632 |
|
| \begin{align*}
x^{\prime }&=x+y+z \\
y^{\prime }&=2 x+5 y+3 z \\
z^{\prime }&=3 x+9 y+5 z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= -1 \\
z \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.559 |
|
| \begin{align*}
x^{\prime \prime }&=y+4 \,{\mathrm e}^{-2 t} \\
y^{\prime \prime }&=x-{\mathrm e}^{-2 t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.047 |
|
| \begin{align*}
x^{\prime }+6 x+3 y^{\prime }+2 y&=0 \\
x^{\prime }+5 x+2 y^{\prime }+3 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 4 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.837 |
|
| \begin{align*}
x^{\prime }-x+2 y^{\prime }+7 y&=0 \\
2 x^{\prime }+y^{\prime }+x+5 y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| \begin{align*}
x^{\prime }+5 x+3 y^{\prime }-11 y&=0 \\
x^{\prime }+3 x+y^{\prime }-7 y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.972 |
|
| \begin{align*}
x^{\prime }-2 x+4 y&=0 \\
3 x+2 y^{\prime }+y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.860 |
|
| \begin{align*}
x^{\prime }+3 x+2 y&=0 \\
3 x+y^{\prime }+y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.162 |
|
| \begin{align*}
x^{\prime }+4 x+3 y^{\prime }+4 y&=0 \\
x^{\prime }+2 x+2 y^{\prime }+2 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 6 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| \begin{align*}
x^{\prime }+x+2 y^{\prime }+3 y&=0 \\
x^{\prime }-2 x+5 y^{\prime }&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.101 |
|
| \begin{align*}
x^{\prime }-x-y&=0 \\
5 x+y^{\prime }-3 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.124 |
|
| \begin{align*}
2 x-y^{\prime }-5 y&=0 \\
x^{\prime }+x+2 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= -10 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| \begin{align*}
2 x^{\prime }-6 x+3 y^{\prime }-2 y&=0 \\
7 x^{\prime }+4 x+7 y^{\prime }+20 y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.979 |
|
| \begin{align*}
x^{\prime }+x+2 y&=8 \\
2 x+y^{\prime }-2 y&=2 \,{\mathrm e}^{-t}-8 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.269 |
|
| \begin{align*}
x^{\prime }+2 y&=4 \,{\mathrm e}^{2 t} \\
x+y^{\prime }-y&=2 \,{\mathrm e}^{2 t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 7 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.171 |
|
| \begin{align*}
x^{\prime }-x+2 y^{\prime }+7 y&=3 t -15 \\
2 x^{\prime }+y^{\prime }+x+5 y&=9 t -7 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= -3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| \begin{align*}
x^{\prime }+3 x-y^{\prime }-y&=0 \\
2 x^{\prime }-9 x+y^{\prime }+4 y&=15 \,{\mathrm e}^{-3 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| \begin{align*}
3 x-y^{\prime }-2 y&=8 t \\
x^{\prime }-2 x+y&=16 \,{\mathrm e}^{-t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.423 |
|
| \begin{align*}
2 x^{\prime }-x-y^{\prime }+y&=4 t \,{\mathrm e}^{-t}-3 \,{\mathrm e}^{-t} \\
x^{\prime }+4 x-2 y^{\prime }-4 y&=2 t \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{-t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.382 |
|
| \begin{align*}
2 x^{\prime }-x+7 y^{\prime }+3 y&=90 \sin \left (2 t \right ) \\
x^{\prime }-5 x+8 y^{\prime }-3 y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.865 |
|
| \begin{align*}
x^{\prime \prime }&=y+4 \,{\mathrm e}^{-2 t} \\
y^{\prime \prime }&=x-{\mathrm e}^{-2 t} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.085 |
|
| \begin{align*}
x^{\prime }-5 x+y^{\prime }+2 z&=24 \,{\mathrm e}^{-t} \\
x^{\prime }-x-y&=0 \\
5 y^{\prime }-11 y+2 z^{\prime }-2 z&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.115 |
|
| \begin{align*}
x^{\prime }+3 x-2 y&={\mathrm e}^{-t} \\
y^{\prime }-x+4 y&=\sin \left (2 t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.491 |
|
| \begin{align*}
x^{\prime }-x+2 y-z&=t^{2} \\
y^{\prime }+3 x-y+4 z&={\mathrm e}^{t} \\
z^{\prime }-2 x+y-z&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
81.501 |
|
| \begin{align*}
z+x^{\prime }&=x \\
y^{\prime }-2 x&=y+3 t \\
z^{\prime }+4 y&=z-\cos \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
5.049 |
|
| \begin{align*}
x^{\prime }+5 x-4 y&=0 \\
y^{\prime }-x+2 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= -2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \begin{align*}
x^{\prime }+x-5 y&=0 \\
y^{\prime }+4 x+5 y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.074 |
|
| \begin{align*}
x^{\prime }-2 x+3 y&=0 \\
-2 x+y^{\prime }+3 y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| \begin{align*}
x^{\prime }+3 x-6 y&=0 \\
y^{\prime }&=x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.959 |
|
| \begin{align*}
x^{\prime }&=x+8 y \\
y^{\prime }&=-2 x-7 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| \begin{align*}
x^{\prime }&=-12 x-7 y \\
y^{\prime }&=19 x+11 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
3.405 |
|
| \begin{align*}
x^{\prime }-y&=t \\
x+y^{\prime }&=t^{2} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.138 |
|
| \begin{align*}
x^{\prime }+3 x+4 y&=8 \,{\mathrm e}^{t} \\
-x+y^{\prime }-y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.068 |
|
| \begin{align*}
x^{\prime }-2 x+y&={\mathrm e}^{-t} \\
y^{\prime }-3 x+2 y&=t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.432 |
|
| \begin{align*}
x^{\prime }+2 x-y&=100 \sin \left (t \right ) \\
y^{\prime }-4 x-y&=36 t \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -8 \\
y \left (0\right ) &= -21 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.421 |
|
| \begin{align*}
x^{\prime }-3 x-6 y&=9-9 t \\
y^{\prime }+3 x+3 y&=9 t \,{\mathrm e}^{-3 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.600 |
|
| \begin{align*}
x^{\prime }&=2 x-3 y+t \,{\mathrm e}^{-t} \\
y^{\prime }&=2 x-3 y+{\mathrm e}^{-t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.174 |
|
| \begin{align*}
x^{\prime }+4 x+2 y-z&=12 \,{\mathrm e}^{t} \\
y^{\prime }-2 x-5 y+3 z&=0 \\
z^{\prime }+4 x+z&=30 \,{\mathrm e}^{-t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.289 |
|
| \begin{align*}
y y^{\prime }&=x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.799 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=y+1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.490 |
|
| \begin{align*}
1+y^{2}&=\left (x^{2}+1\right ) y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.913 |
|
| \begin{align*}
y^{\prime } \sin \left (y\right )&=\sec \left (x \right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.165 |
|
| \begin{align*}
x^{\prime }&=\frac {x}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.656 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=1-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.932 |
|
| \begin{align*}
\frac {\tan \left (y\right )}{\cos \left (x \right )}&=\cos \left (x \right ) y^{\prime } \\
y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.020 |
|
| \begin{align*}
x y^{\prime }&=\left (x +1\right ) y^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.296 |
|
| \begin{align*}
x \cos \left (y\right ) y^{\prime }-\left (x^{2}+1\right ) \sin \left (y\right )&=0 \\
y \left (1\right ) &= \frac {\pi }{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.661 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }&=\left (-1+y\right ) x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.425 |
|
| \begin{align*}
\left (y+2\right ) x +y \left (x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
26.763 |
|
| \begin{align*}
x y \left (x^{2}+1\right ) y^{\prime }-y^{2}&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
24.758 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.985 |
|
| \begin{align*}
x y^{\prime }-1+y&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.740 |
|
| \begin{align*}
-x y^{\prime }+y&=3 y^{2} y^{\prime } \\
y \left (3\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
52.197 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.663 |
|
| \begin{align*}
x \cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.299 |
|
| \begin{align*}
y^{\prime }&=\frac {\sin \left (x \right ) \sin \left (y\right )}{\cos \left (x \right ) \cos \left (y\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.385 |
|
| \begin{align*}
x \sec \left (y\right )^{2} y^{\prime }+1+\tan \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
49.997 |
|
| \begin{align*}
{\mathrm e}^{y} \left (x y^{\prime }+1\right )&=5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.274 |
|
| \begin{align*}
{\mathrm e}^{x} \left (y^{\prime }+y\right )&=3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.456 |
|
| \begin{align*}
\frac {y}{x}+\ln \left (x \right ) y^{\prime }&=2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.052 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
57.458 |
|
| \begin{align*}
y^{\prime }&=1+\frac {y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.797 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.235 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\frac {x}{y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.312 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y+1}{x +y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
43.102 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y+2}{x +1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.687 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+2}{x +1} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.246 |
|
| \begin{align*}
y^{\prime }+3 y&=5 \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.543 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.365 |
|
| \begin{align*}
y^{\prime }-2 y x&=3 x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.562 |
|
| \begin{align*}
y^{\prime }+7 y&={\mathrm e}^{5 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.307 |
|
| \begin{align*}
y^{\prime }-6 y&={\mathrm e}^{6 t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.596 |
|
| \begin{align*}
y^{\prime }-6 y&={\mathrm e}^{6 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.153 |
|
| \begin{align*}
z^{\prime }-z \sin \left (x \right )&={\mathrm e}^{-\cos \left (x \right )} \\
z \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
26.236 |
|
| \begin{align*}
z^{\prime }-z \sin \left (x \right )&={\mathrm e}^{-\cos \left (x \right )} \\
z \left (2 \pi \right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
25.707 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=5 x \\
y \left ({\mathrm e}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.053 |
|
| \begin{align*}
y^{\prime }-\frac {6 y}{x}&=7 x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
13.011 |
|
| \begin{align*}
y^{\prime }-y \sin \left (x \right )&=\sin \left (x \right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.102 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=\sec \left (x \right ) \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.093 |
|
| \begin{align*}
\left (1+{\mathrm e}^{x}\right ) y^{\prime }+y \,{\mathrm e}^{x}&={\mathrm e}^{x} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.290 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x&=\left (x^{2}+1\right )^{{3}/{2}} \\
y \left (0\right ) &= 7 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.497 |
|
| \begin{align*}
p^{\prime }&=15-20 p \\
p \left (0\right ) &= {\frac {7}{10}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.839 |
|
| \begin{align*}
n^{\prime }&=k n-b t \\
n \left (0\right ) &= n_{0} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.663 |
|
| \begin{align*}
x y^{\prime }-2 \cos \left (x \right ) y&={\mathrm e}^{x} \sin \left (x \right )^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
29.998 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }+2 \cos \left (x \right ) y&=4 \cos \left (x \right )^{3} \\
y \left (\frac {\pi }{4}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.862 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +a^{2}}{a^{2}-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.122 |
|
| \begin{align*}
y^{\prime }+\frac {y \ln \left (x \right )}{x}&=2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.564 |
|
| \begin{align*}
y^{\prime }+4 y&={\mathrm e}^{k x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.975 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.948 |
|
| \begin{align*}
v^{\prime }&=60 t -4 v \\
v \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.122 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.450 |
|