| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+z\\ y^{\prime }&=x+z\\ z^{\prime }&=x+y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.260 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x-5 y&=0\\ y^{\prime }+4 x+5 y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.229 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 y^{\prime }+y&={\mathrm e}^{t}\\ -x+y^{\prime }&=y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.233 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-3 x-6 y&=27 t^{2}\\ x^{\prime }+y^{\prime }-3 y&=5 \,{\mathrm e}^{t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.291 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=-2 y\\ y^{\prime }&=y-x^{\prime }\\ \end {array} \]
|
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.034 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=x-2\\ x^{\prime \prime }&=2+y\\ \end {array} \]
|
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.032 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }&=\cos \left (t \right )\\ x+y^{\prime \prime }&=2\\ \end {array} \]
|
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=x-y\\ z^{\prime }&=2 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.367 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y+z\\ y^{\prime }&=2 x+5 y+3 z\\ z^{\prime }&=3 x+9 y+5 z\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.462 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=y+4 \,{\mathrm e}^{-2 t}\\ y^{\prime \prime }&=x-{\mathrm e}^{-2 t}\\ \end {array} \]
|
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.035 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+6 x+3 y^{\prime }+2 y&=0\\ x^{\prime }+5 x+2 y^{\prime }+3 y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x+2 y^{\prime }+7 y&=0\\ 2 x^{\prime }+y^{\prime }+x+5 y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+5 x+3 y^{\prime }-11 y&=0\\ x^{\prime }+3 x+y^{\prime }-7 y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
4.361 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-2 x+4 y&=0\\ 3 x+2 y^{\prime }+y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 x+2 y&=0\\ 3 x+y^{\prime }+y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.748 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+4 x+3 y^{\prime }+4 y&=0\\ x^{\prime }+2 x+2 y^{\prime }+2 y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x+2 y^{\prime }+3 y&=0\\ x^{\prime }-2 x+5 y^{\prime }&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x-y&=0\\ 5 x+y^{\prime }-3 y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x-y^{\prime }-5 y&=0\\ x^{\prime }+x+2 y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }-6 x+3 y^{\prime }-2 y&=0\\ 7 x^{\prime }+4 x+7 y^{\prime }+20 y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x+2 y&=8\\ 2 x+y^{\prime }-2 y&=2 \,{\mathrm e}^{-t}-8\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.956 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 y&=4 \,{\mathrm e}^{2 t}\\ x+y^{\prime }-y&=2 \,{\mathrm e}^{2 t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x+2 y^{\prime }+7 y&=3 t -15\\ 2 x^{\prime }+y^{\prime }+x+5 y&=9 t -7\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.755 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 x-y^{\prime }-y&=0\\ 2 x^{\prime }-9 x+y^{\prime }+4 y&=15 \,{\mathrm e}^{-3 t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x-y^{\prime }-2 y&=8 t\\ x^{\prime }-2 x+y&=16 \,{\mathrm e}^{-t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.094 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }-x-y^{\prime }+y&=4 t \,{\mathrm e}^{-t}-3 \,{\mathrm e}^{-t}\\ x^{\prime }+4 x-2 y^{\prime }-4 y&=2 t \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{-t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.896 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }-x+7 y^{\prime }+3 y&=90 \sin \left (2 t \right )\\ x^{\prime }-5 x+8 y^{\prime }-3 y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.455 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=y+4 \,{\mathrm e}^{-2 t}\\ y^{\prime \prime }&=x-{\mathrm e}^{-2 t}\\ \end {array} \]
|
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-5 x+y^{\prime }+2 z&=24 \,{\mathrm e}^{-t}\\ x^{\prime }-x-y&=0\\ 5 y^{\prime }-11 y+2 z^{\prime }-2 z&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.583 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 x-2 y&={\mathrm e}^{-t}\\ y^{\prime }-x+4 y&=\sin \left (2 t \right )\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.187 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x+2 y-z&=t^{2}\\ y^{\prime }+3 x-y+4 z&={\mathrm e}^{t}\\ z^{\prime }-2 x+y-z&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
69.499 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z+x^{\prime }&=x\\ y^{\prime }-2 x&=y+3 t\\ z^{\prime }+4 y&=z-\cos \left (t \right )\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
3.360 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+5 x-4 y&=0\\ y^{\prime }-x+2 y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
4.941 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x-5 y&=0\\ y^{\prime }+4 x+5 y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-2 x+3 y&=0\\ -2 x+y^{\prime }+3 y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.466 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 x-6 y&=0\\ y^{\prime }&=x-3 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+8 y\\ y^{\prime }&=-2 x-7 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-12 x-7 y\\ y^{\prime }&=19 x+11 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.238 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-y&=t\\ x+y^{\prime }&=t^{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 x+4 y&=8 \,{\mathrm e}^{t}\\ -x+y^{\prime }-y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.741 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-2 x+y&={\mathrm e}^{-t}\\ y^{\prime }-3 x+2 y&=t\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 x-y&=100 \sin \left (t \right )\\ y^{\prime }-4 x-y&=36 t\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-3 x-6 y&=9-9 t\\ y^{\prime }+3 x+3 y&=9 t \,{\mathrm e}^{-3 t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.245 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-3 y+t \,{\mathrm e}^{-t}\\ y^{\prime }&=2 x-3 y+{\mathrm e}^{-t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+4 x+2 y-z&=12 \,{\mathrm e}^{t}\\ y^{\prime }-2 x-5 y+3 z&=0\\ z^{\prime }+4 x+z&=30 \,{\mathrm e}^{-t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.823 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime }&=x^{2} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.967 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right ) y^{\prime }&=1+y \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.321 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 1+y^{2}&=\left (x^{2}+1\right ) y^{\prime } \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.084 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } \sin \left (y\right )&=\sec \left (x \right )^{2} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
75.367 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {x}{t} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.493 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime }&=1-y^{2}\\ y \left (0\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.939 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {\tan \left (y\right )}{\cos \left (x \right )}&=\cos \left (x \right ) y^{\prime }\\ y \left (\frac {\pi }{4}\right )&=\frac {\pi }{2}\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.281 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&=\left (x +1\right ) y^{2}\\ y \left (1\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.180 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \cos \left (y\right ) y^{\prime }-\left (x^{2}+1\right ) \sin \left (y\right )&=0\\ y \left (1\right )&=\frac {\pi }{2}\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.037 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime }&=\left (-1+y\right ) x \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.562 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (y+2\right ) x +y \left (2+x \right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.723 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y \left (x^{2}+1\right ) y^{\prime }-y^{2}&=1 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.158 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +y&=0\\ y \left (1\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.136 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -1+y&=0\\ y \left (1\right )&=2\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.958 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-y^{\prime } x&=3 y^{2} y^{\prime }\\ y \left (3\right )&=1\\ \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
60.289 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+2 y x&=0\\ y \left (1\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.584 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=5 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.110 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\sin \left (x \right ) \sin \left (y\right )}{\cos \left (x \right ) \cos \left (y\right )} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.412 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \sec \left (y\right )^{2} y^{\prime }+1+\tan \left (y\right )&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
32.150 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{y} \left (y^{\prime } x +1\right )&=5 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
88.092 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{x} \left (y^{\prime }+y\right )&=3 \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.518 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {y}{x}+\ln \left (x \right ) y^{\prime }&=2 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.709 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {x -y}{x +y} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
141.199 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=1+\frac {y}{x} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.619 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.710 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y}{x}-\frac {x}{y} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.422 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {x -y+1}{x +y+1} \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
268.525 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {x -y+2}{x +1} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.289 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {x +y+2}{x +1}\\ y \left (0\right )&=-1\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.374 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+3 y&=5\\ y \left (0\right )&=y_{0}\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.350 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y x&=x\\ y \left (0\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.720 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-2 y x&=3 x\\ y \left (1\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.797 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+7 y&={\mathrm e}^{5 x}\\ y \left (0\right )&=0\\ \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
80.240 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-6 y&={\mathrm e}^{6 t}\\ y \left (0\right )&=0\\ \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
103.765 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-6 y&={\mathrm e}^{6 t}\\ y \left (0\right )&=1\\ \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
98.146 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{\prime }-z \sin \left (x \right )&={\mathrm e}^{-\cos \left (x \right )}\\ z \left (0\right )&=0\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
63.520 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{\prime }-z \sin \left (x \right )&={\mathrm e}^{-\cos \left (x \right )}\\ z \left (2 \pi \right )&=2\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
34.296 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-\frac {3 y}{x}&=5 x\\ y \left ({\mathrm e}\right )&=0\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.772 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-\frac {6 y}{x}&=7 x\\ y \left (1\right )&=0\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
15.416 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-\sin \left (x \right ) y&=\sin \left (x \right )\\ y \left (0\right )&=2\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.705 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\tan \left (x \right ) y&=\sec \left (x \right )\\ y \left (0\right )&=5\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.229 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left ({\mathrm e}^{x}+1\right ) y^{\prime }+{\mathrm e}^{x} y&={\mathrm e}^{x}\\ y \left (0\right )&=2\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.080 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime }+y x&=\left (x^{2}+1\right )^{{3}/{2}}\\ y \left (0\right )&=7\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.290 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} p^{\prime }&=15-20 p\\ p \left (0\right )&={\frac {7}{10}}\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.079 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} n^{\prime }&=k n-b t\\ n \left (0\right )&=n_{0}\\ \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.750 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -2 \cos \left (x \right ) y&={\mathrm e}^{x} \sin \left (x \right )^{3} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✗ |
35.958 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x \right ) y^{\prime }+2 \cos \left (x \right ) y&=4 \cos \left (x \right )^{3}\\ y \left (\frac {\pi }{4}\right )&=1\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
142.787 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y x +a^{2}}{a^{2}-x^{2}} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.934 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\frac {y \ln \left (x \right )}{x}&=2 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.556 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+4 y&={\mathrm e}^{k x} \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.086 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y&=x \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.017 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} v^{\prime }&=60 t -4 v\\ v \left (0\right )&=0\\ \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.127 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.255 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.261 |
|