| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{2} y+\left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
✗ |
40.078 |
|
| \begin{align*}
x y^{2}+\left (3-2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
51.753 |
|
| \begin{align*}
y+2 x^{3}+\left (2 x -\frac {x^{4}}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
38.785 |
|
| \begin{align*}
x^{3}+y^{2}+\left (y x -3 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
67.807 |
|
| \begin{align*}
y^{\prime }+3 y&=x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.105 |
|
| \begin{align*}
y^{\prime }-2 y&=\cos \left (3 x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.713 |
|
| \begin{align*}
y^{\prime }-y&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.947 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=-x^{2}+1 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.928 |
|
| \begin{align*}
y^{\prime }+x^{2} y&=\left (x^{2}+1\right ) {\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.710 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\ln \left (x \right )-2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.417 |
|
| \begin{align*}
y^{\prime }-\tan \left (x \right ) y&=\sin \left (x \right ) \\
y \left (\frac {\pi }{4}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.296 |
|
| \begin{align*}
y^{\prime }-\frac {y}{-x^{2}+1}&=3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.563 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=\cot \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.701 |
|
| \begin{align*}
y^{\prime }-y x&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.464 |
|
| \begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.745 |
|
| \begin{align*}
y^{\prime }-4 y&=x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.103 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=\frac {x^{2}}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
24.787 |
|
| \begin{align*}
y^{5} y^{\prime }+5 y^{6}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.470 |
|
| \begin{align*}
y^{\prime }+y x&=x y^{5} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.851 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.130 |
|
| \begin{align*}
y^{\prime \prime } x&=x^{2}+1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.965 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| \begin{align*}
\left (2+x \right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.277 |
|
| \begin{align*}
3 y y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.690 |
|
| \begin{align*}
y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
5.638 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x&=2 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| \begin{align*}
y^{\prime \prime } x +x {y^{\prime }}^{2}-y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.916 |
|
| \begin{align*}
6 y^{\prime \prime }+11 y^{\prime }+4 y&=2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \begin{align*}
3 y^{\prime \prime }-4 y^{\prime }+y&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
y^{\prime \prime }-k^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.224 |
|
| \begin{align*}
y^{\prime \prime }+k^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.511 |
|
| \begin{align*}
y^{\prime }&=-2 \\
z^{\prime }&=x \,{\mathrm e}^{2 x +y} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.053 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{x} \\
z^{\prime }&=y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.568 |
|
| \begin{align*}
y^{\prime }&=z \\
z^{\prime }&=y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \begin{align*}
y y^{\prime }&=-x \\
y z^{\prime }&=2 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| \begin{align*}
y^{\prime }+2 z&=y \\
z^{\prime }+4 y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| \begin{align*}
y^{\prime }&=x +2 z \\
z^{\prime }&=3 x +y-z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| \begin{align*}
y^{\prime }&=x^{2}+6 y+4 z \\
z^{\prime }&=y+3 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| \begin{align*}
y^{\prime }&=y+z+x \\
z^{\prime }&=1-y-z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right )+a y+b z \\
z^{\prime }&=g \left (x \right )+c y+d z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
4.368 |
|
| \begin{align*}
y^{\prime }&=x^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.193 |
|
| \begin{align*}
y \cos \left (y x \right )+y-x +\left (x \cos \left (y x \right )+x -y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.858 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.082 |
|
| \begin{align*}
x -y+1+\left (2 y-2 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.111 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{5}+y x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
10.325 |
|
| \begin{align*}
y^{5} x^{2}+{\mathrm e}^{x^{3}} y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.985 |
|
| \begin{align*}
\left (x +2 y+2\right ) y^{\prime }&=3 x -y-1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.921 |
|
| \begin{align*}
x \sqrt {a^{2}+x^{2}}&=y \sqrt {y^{2}-a^{2}}\, y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.607 |
|
| \begin{align*}
{\mathrm e}^{x} \cos \left (y\right )+x -\left ({\mathrm e}^{x} \sin \left (y\right )+y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
5.856 |
|
| \begin{align*}
1+\left (1-3 x +y\right ) y^{\prime }&=0 \\
y \left (4\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.125 |
|
| \begin{align*}
y^{\prime } x&=y \\
z^{\prime }&=3 y-x \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.043 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.135 |
|
| \begin{align*}
\left (x +\frac {x}{x^{2}+y^{2}}\right ) y^{\prime }+y-\frac {y}{x^{2}+y^{2}}&=0 \\
y \left (1\right ) &= \sqrt {3} \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
3.721 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{3} x \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
2.306 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{y-y^{3}+2 x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
3.184 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right )^{3} \cos \left (x \right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.329 |
|
| \begin{align*}
y x -x&=\left (x y^{2}+x -y^{2}-1\right ) y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.447 |
|
| \begin{align*}
x^{2} y+2 y^{3}-\left (2 x^{3}+3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
29.053 |
|
| \begin{align*}
y y^{\prime } x +2 x +\frac {y^{2}}{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.871 |
|
| \begin{align*}
2 x y^{2}+\left (1-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
48.588 |
|
| \begin{align*}
x^{2} y^{\prime }-y^{2}&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.826 |
|
| \begin{align*}
y^{\prime }&=z \\
z^{\prime }&=w \\
w^{\prime }&=y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.654 |
|
| \begin{align*}
{\mathrm e}^{2 x +3 y}+{\mathrm e}^{4 x -5 y} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.167 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.874 |
|
| \begin{align*}
3 y^{2}-2 x^{2}&=2 y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
72.783 |
|
| \begin{align*}
\left (2+3 y\right ) y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.753 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
y^{\prime }-2 y&=x^{2}-1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.076 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{2}&=x^{4} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.011 |
|
| \begin{align*}
y^{\prime }-5 y&=3 x^{3}+4 x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.665 |
|
| \begin{align*}
y^{\prime }-y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.690 |
|
| \begin{align*}
y^{\prime }-y x&=-x^{5}+4 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.424 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.370 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.237 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.598 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.487 |
|
| \begin{align*}
y^{\prime \prime }+k y^{\prime }+L y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| \begin{align*}
y^{\prime \prime }+\frac {327 y^{\prime }}{100}-\frac {21 y}{50}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }-6 y&=x^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=x^{2}-2 x +1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=1-x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.646 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.427 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=2 \,{\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.689 |
|
| \begin{align*}
y^{\prime \prime }-9 y&={\mathrm e}^{x}+3 \,{\mathrm e}^{-3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=1+2 x +3 \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| \begin{align*}
y^{\prime \prime }-\left (m_{1} +m_{2} \right ) y^{\prime }+m_{1} m_{2} y&={\mathrm e}^{x m} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.062 |
|
| \begin{align*}
y^{\left (8\right )}-y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| \begin{align*}
y^{\prime \prime \prime }-y&=1 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.133 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&={\mathrm e}^{-2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y^{\prime \prime }&=x^{3} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.178 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=x +{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| \begin{align*}
y^{\left (5\right )}-y^{\prime \prime \prime \prime }+2 y^{\prime }-y&=x^{4}-2 x +1 \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.239 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y&=\sin \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.161 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime }&={\mathrm e}^{x}+1 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.174 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=x^{4} {\mathrm e}^{2 x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.219 |
|
| \begin{align*}
y^{\left (6\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }+y&=\cos \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.434 |
|