| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
3 x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.389 |
|
| \begin{align*}
y x -2 y^{2}-\left (x^{2}-3 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
1.228 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.186 |
|
| \begin{align*}
2 y-3 x y^{2}-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.343 |
|
| \begin{align*}
y+x \left (x^{2} y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
0.472 |
|
| \begin{align*}
y+x^{3} y+2 x^{2}+\left (x +4 y^{4} x +8 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
0.525 |
|
| \begin{align*}
-y-{\mathrm e}^{x} x^{2}+y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.295 |
|
| \begin{align*}
1+y^{2}&=\left (x^{2}+x \right ) y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.408 |
|
| \begin{align*}
2 y-x^{3}+y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| \begin{align*}
y+\left (y^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.655 |
|
| \begin{align*}
3 y^{3}-y x -\left (x^{2}+6 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
1.168 |
|
| \begin{align*}
3 y^{2} x^{2}+4 \left (x^{3} y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
0.466 |
|
| \begin{align*}
y \left (x +y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
2 y+3 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
1.181 |
|
| \begin{align*}
y \left (y^{2}-2 x^{2}\right )+x \left (2 y^{2}-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.060 |
|
| \begin{align*}
-y+y^{\prime } x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.271 |
|
| \begin{align*}
y^{\prime }+y&=2 x +2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.869 |
|
| \begin{align*}
y^{\prime }-y&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.751 |
|
| \begin{align*}
-3 y-\left (x -2\right ) {\mathrm e}^{x}+y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.219 |
|
| \begin{align*}
i^{\prime }-6 i&=10 \sin \left (2 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.850 |
|
| \begin{align*}
y^{\prime }+y&=y^{2} {\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.278 |
|
| \begin{align*}
y+\left (y x +x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
3.954 |
|
| \begin{align*}
\left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime }&=2 s \,{\mathrm e}^{2 t}-2 \cos \left (2 t \right ) \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
17.585 |
|
| \begin{align*}
y^{\prime } x +y-x^{3} y^{6}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.694 |
|
| \begin{align*}
r^{\prime }+2 r \cos \left (\theta \right )+\sin \left (2 \theta \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.679 |
|
| \begin{align*}
y \left (1+y^{2}\right )&=2 \left (1-2 x y^{2}\right ) y^{\prime } \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
3.239 |
|
| \begin{align*}
y y^{\prime }-x y^{2}+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.781 |
|
| \begin{align*}
\left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
3.936 |
|
| \begin{align*}
2 x^{\prime }-\frac {x}{y}+x^{3} \cos \left (y \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.150 |
|
| \begin{align*}
y^{\prime } x&=y \left (1-x \tan \left (x \right )\right )+x^{2} \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
20.475 |
|
| \begin{align*}
2+y^{2}-\left (y x +2 y+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
9.817 |
|
| \begin{align*}
1+y^{2}&=\left (\arctan \left (y\right )-x \right ) y^{\prime } \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.227 |
|
| \begin{align*}
2 x y^{5}-y+2 y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.913 |
|
| \begin{align*}
1+\sin \left (y\right )&=\left (2 y \cos \left (y\right )-x \left (\sec \left (y\right )+\tan \left (y\right )\right )\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
6.225 |
|
| \begin{align*}
y^{\prime } x&=2 y+{\mathrm e}^{x} x^{3} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.689 |
|
| \begin{align*}
L i^{\prime }+R i&=E \sin \left (2 t \right ) \\
i \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.185 |
|
| \begin{align*}
x^{2} y^{\prime } \cos \left (y\right )&=2 x \sin \left (y\right )-1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
4.409 |
|
| \begin{align*}
4 x^{2} y y^{\prime }&=3 x \left (3 y^{2}+2\right )+2 \left (3 y^{2}+2\right )^{3} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✓ |
22.649 |
|
| \begin{align*}
x y^{3}-y^{3}-{\mathrm e}^{x} x^{2}+3 y^{\prime } y^{2} x&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.477 |
|
| \begin{align*}
y^{\prime }+x \left (x +y\right )&=x^{3} \left (x +y\right )^{3}-1 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✓ |
4.462 |
|
| \begin{align*}
y+{\mathrm e}^{y}-{\mathrm e}^{-x}+\left (1+{\mathrm e}^{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
3.509 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+y y^{\prime } x -6 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.455 |
|
| \begin{align*}
x {y^{\prime }}^{2}+\left (y-1-x^{2}\right ) y^{\prime }-\left (-1+y\right ) x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.995 |
|
| \begin{align*}
3 x^{4} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
1.676 |
|
| \begin{align*}
8 y {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.856 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
0.744 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \begin{align*}
16 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
0.772 |
|
| \begin{align*}
x {y^{\prime }}^{5}-y {y^{\prime }}^{4}+\left (x^{2}+1\right ) {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+\left (x +y^{2}\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.527 |
|
| \begin{align*}
x {y^{\prime }}^{2}-y y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.824 |
|
| \begin{align*}
y&=2 y^{\prime } x +y^{2} {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.717 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.173 |
|
| \begin{align*}
y&=x \left (1+y^{\prime }\right )+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.949 |
|
| \begin{align*}
y&=2 y^{\prime }+\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
20.718 |
|
| \begin{align*}
y {y^{\prime }}^{2}-y^{\prime } x +3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.386 |
|
| \begin{align*}
y&=y^{\prime } x -2 {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
0.605 |
|
| \begin{align*}
4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.903 |
|
| \begin{align*}
x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.190 |
|
| \begin{align*}
\left (3 y-1\right )^{2} {y^{\prime }}^{2}&=4 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.753 |
|
| \begin{align*}
y&=-y^{\prime } x +x^{4} {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
1.759 |
|
| \begin{align*}
2 y&={y^{\prime }}^{2}+4 y^{\prime } x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.922 |
|
| \begin{align*}
y \left (3-4 y\right )^{2} {y^{\prime }}^{2}&=4-4 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| \begin{align*}
{y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
0.583 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) \left (x -y\right )^{2}&=\left (x +y y^{\prime }\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
120.396 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.269 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.054 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{5 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\cos \left (x \right ) x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.875 |
|
| \begin{align*}
-y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=3 x^{4} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.310 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.979 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
3.141 |
|
| \begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=2 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
2.841 |
|
| \begin{align*}
{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
0.692 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-15 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.295 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.045 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+12 y^{\prime \prime }-8 y^{\prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
y^{\prime \prime }+25 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.159 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+9 y^{\prime }-9 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.054 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.062 |
|
| \begin{align*}
y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.079 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }&=5 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.913 |
|
| \begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }&=5 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.097 |
|
| \begin{align*}
y^{\left (5\right )}-4 y^{\prime \prime \prime }&=5 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.116 |
|
| \begin{align*}
-4 y^{\prime }+y^{\prime \prime \prime }&=x \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.099 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=-2 x^{2}+2 x +2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.403 |
|
| \begin{align*}
y^{\prime \prime }-y&=4 x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
y^{\prime \prime }-y&=\sin \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \begin{align*}
y^{\prime \prime }-y&=\frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.747 |
|
| \begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.508 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\sin \left ({\mathrm e}^{-x}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.508 |
|
| \begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.439 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=4 \sec \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.724 |
|