| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
{y^{\prime \prime }}^{3}+y^{\prime \prime }+1&=x \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✗ |
✓ |
200.805 |
|
| \begin{align*}
x^{\prime \prime }+10 x^{\prime }+25 x&=2^{t}+t \,{\mathrm e}^{-5 t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \begin{align*}
-y y^{\prime }-x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\
\end{align*} |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.268 |
|
| \begin{align*}
y^{\left (6\right )}-y&={\mathrm e}^{2 x} \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.134 |
|
| \begin{align*}
y^{\left (6\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime }&=x +{\mathrm e}^{x} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.144 |
|
| \begin{align*}
6 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2}&=0 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✗ |
0.440 |
|
| \begin{align*}
y^{\prime \prime } x&=y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) \sin \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \begin{align*}
y^{\prime \prime }&=2 y^{3} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
1.786 |
|
| \begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.291 |
|
| \begin{align*}
x^{\prime }&=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 |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
x^{\prime }+5 x+y&={\mathrm e}^{t} \\
y^{\prime }-x-3 y&={\mathrm e}^{2 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.674 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.029 |
|
| \begin{align*}
y^{\prime }&=y \,{\mathrm e}^{x +y} \left (x^{2}+1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.892 |
|
| \begin{align*}
x^{2} y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.918 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
1.782 |
|
| \begin{align*}
x \left ({\mathrm e}^{y}+4\right )&={\mathrm e}^{x +y} y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.494 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.160 |
|
| \begin{align*}
y^{\prime } x +y&=x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.919 |
|
| \begin{align*}
y^{\prime }&=t \ln \left (y^{2 t}\right )+t^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✓ |
✗ |
20.394 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{y^{2}-x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.636 |
|
| \begin{align*}
y^{\prime }&=\ln \left (y x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
2.298 |
|
| \begin{align*}
x \left (1+y\right )^{2}&=\left (x^{2}+1\right ) y \,{\mathrm e}^{y} y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.612 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.412 |
|
| \begin{align*}
y^{\prime \prime \prime }+y x&=\sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
0.035 |
|
| \begin{align*}
y y^{\prime }+y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
71.711 |
|
| \begin{align*}
y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime }&=2 x^{2}+3 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.138 |
|
| \begin{align*}
y^{\prime \prime }+y y^{\prime \prime \prime \prime }&=1 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.039 |
|
| \begin{align*}
y^{\prime \prime \prime }+y x&=\cosh \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
0.037 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y \,{\mathrm e}^{x^{2}}&=\sinh \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
25.079 |
|
| \begin{align*}
y^{\prime \prime \prime }+y x&=\cosh \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
0.030 |
|
| \begin{align*}
y y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \begin{align*}
\sinh \left (x \right ) {y^{\prime }}^{2}+3 y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
37.371 |
|
| \begin{align*}
5 y^{\prime }-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.632 |
|
| \begin{align*}
{y^{\prime }}^{2} \sqrt {y}&=\sin \left (x \right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.023 |
|
| \begin{align*}
2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y&=1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
8.295 |
|
| \begin{align*}
y^{\prime \prime \prime }&=1 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.069 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y&=\sin \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.878 |
|
| \begin{align*}
y^{\prime \prime }&=y+x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.247 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime } x -y^{2}&=\sin \left (x \right ) \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.034 |
|
| \begin{align*}
{y^{\prime }}^{2}+x y {y^{\prime }}^{2}&=\ln \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
41.583 |
|
| \begin{align*}
\sin \left (y^{\prime \prime }\right )+y y^{\prime \prime \prime \prime }&=1 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.031 |
|
| \begin{align*}
\sinh \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime }&=y x \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
1.239 |
|
| \begin{align*}
y y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
0.474 |
|
| \begin{align*}
{y^{\prime \prime \prime }}^{2}+\sqrt {y}&=\sin \left (x \right ) \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.058 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.183 |
|
| \begin{align*}
y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.072 |
|
| \begin{align*}
2 y^{\prime \prime }-3 y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.159 |
|
| \begin{align*}
3 y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| \begin{align*}
\left (x -3\right ) y^{\prime \prime }+y \ln \left (x \right )&=x^{2} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
27.014 |
|
| \begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cot \left (x \right ) y&=0 \\
y \left (\frac {\pi }{4}\right ) &= 1 \\
y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
6.833 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
60.009 |
|
| \begin{align*}
y^{\prime \prime } x +2 x^{2} y^{\prime }+\sin \left (x \right ) y&=\sinh \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
54.867 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime \prime }+y^{\prime } x +7 y&=1 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
21.411 |
|
| \begin{align*}
y^{\prime \prime }-\left (x -1\right ) y^{\prime }+x^{2} y&=\tan \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
10.687 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.603 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
9.649 |
|
| \begin{align*}
y^{\prime \prime }+\frac {k x}{y^{4}}&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
0.635 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.438 |
|
| \begin{align*}
y^{\prime \prime } x +\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✗ |
✗ |
0.441 |
|
| \begin{align*}
y^{\prime \prime }+2 x^{2} y^{\prime }+4 y x&=2 x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.960 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=1-2 x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.893 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.278 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+2 \left (1-x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
8.841 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=2 x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.912 |
|
| \begin{align*}
\ln \left (x^{2}+1\right ) y^{\prime \prime }+\frac {4 x y^{\prime }}{x^{2}+1}+\frac {\left (-x^{2}+1\right ) y}{\left (x^{2}+1\right )^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
308.815 |
|
| \begin{align*}
y^{\prime \prime } x +x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.560 |
|
| \begin{align*}
y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.463 |
|
| \begin{align*}
-\csc \left (x \right )^{2} y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
24.226 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime \prime }+2 y^{\prime }-\frac {y}{x}&=1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.651 |
|
| \begin{align*}
y^{\prime \prime } x +\left (6 x y^{2}+1\right ) y^{\prime }+2 y^{3}+1&=0 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✗ |
✗ |
✗ |
15.494 |
|
| \begin{align*}
\frac {x y^{\prime \prime }}{1+y}+\frac {y y^{\prime }-x {y^{\prime }}^{2}+y^{\prime }}{\left (1+y\right )^{2}}&=x \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.895 |
|
| \begin{align*}
\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime \prime }-x {y^{\prime }}^{2} \sin \left (y\right )+2 \left (\cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }&=\sin \left (x \right ) y \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
✗ |
0.627 |
|
| \begin{align*}
y y^{\prime \prime } \sin \left (x \right )+\left (\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y\right ) y^{\prime }&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.455 |
|
| \begin{align*}
\left (1-y\right ) y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.595 |
|
| \begin{align*}
\left (\cos \left (y\right )-\sin \left (y\right ) y\right ) y^{\prime \prime }-{y^{\prime }}^{2} \left (2 \sin \left (y\right )+y \cos \left (y\right )\right )&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
✗ |
0.652 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 x y^{\prime }}{2 x -1}-\frac {4 x y}{\left (2 x -1\right )^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.398 |
|
| \begin{align*}
\left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime }&=\left (25-6 x \right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.453 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x +1}-\frac {\left (2+x \right ) y}{x^{2} \left (x +1\right )}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.460 |
|
| \begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.428 |
|
| \begin{align*}
\frac {\left (x^{2}-x \right ) y^{\prime \prime }}{x}+\frac {\left (1+3 x \right ) y^{\prime }}{x}+\frac {y}{x}&=3 x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.385 |
|
| \begin{align*}
\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 \cos \left (x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
7.953 |
|
| \begin{align*}
y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x}+\frac {y}{x^{3}}&=\frac {{\mathrm e}^{-\frac {1}{x}}}{x^{3}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
8.987 |
|
| \begin{align*}
y^{\prime \prime }+\left (5+2 x \right ) y^{\prime }+\left (4 x +8\right ) y&={\mathrm e}^{-2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.466 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| \begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.118 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.131 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.107 |
|
| \begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+37 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.145 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.117 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.126 |
|
| \begin{align*}
4 y^{\prime \prime }-12 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.128 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -6 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.089 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= \frac {\sqrt {2}}{2} \\
\end{align*} Using Laplace transform method. |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.125 |
|
| \begin{align*}
y^{\prime \prime }-20 y^{\prime }+51 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -14 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \begin{align*}
2 y^{\prime \prime }+3 y^{\prime }+y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.121 |
|