| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
2.770 |
|
| \begin{align*}
y^{\prime }&=\left (x^{2}+2 y-1\right )^{{2}/{3}}-x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.521 |
|
| \begin{align*}
x y^{\prime }+y&=x^{2} \left (1+{\mathrm e}^{x}\right ) y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.737 |
|
| \begin{align*}
2 y-x y \ln \left (x \right )-2 x \ln \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.756 |
|
| \begin{align*}
y^{\prime }+a y&=k \,{\mathrm e}^{b x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.253 |
|
| \begin{align*}
y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.685 |
|
| \begin{align*}
y^{\prime }+8 x^{3} y^{3}+2 y x&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.799 |
|
| \begin{align*}
\left (x y \sqrt {x^{2}-y^{2}}+x \right ) y^{\prime }&=y-x^{2} \sqrt {x^{2}-y^{2}} \\
\end{align*} |
[NONE] |
✗ |
✓ |
✓ |
✗ |
31.371 |
|
| \begin{align*}
y^{\prime }+a y&=b \sin \left (k x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.115 |
|
| \begin{align*}
x y^{\prime }-y^{2}+1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.609 |
|
| \begin{align*}
\left (y^{2}+a \sin \left (x \right )\right ) y^{\prime }&=\cos \left (x \right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
2.750 |
|
| \begin{align*}
x y^{\prime }&=x +y+{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.734 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&={\mathrm e}^{-\sin \left (x \right )} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.564 |
|
| \begin{align*}
x y^{\prime }-y \left (\ln \left (y x \right )-1\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
3.022 |
|
| \begin{align*}
x^{3} y^{\prime }-y^{2}-x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.497 |
|
| \begin{align*}
x y^{\prime }+a y+b \,x^{n}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.151 |
|
| \begin{align*}
x y^{\prime }-y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.299 |
|
| \begin{align*}
y^{2}-3 y x -2 x^{2}+\left (y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
13.667 |
|
| \begin{align*}
\left (3+6 y x +x^{2}\right ) y^{\prime }+2 x +2 y x +3 y^{2}&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
3.812 |
|
| \begin{align*}
x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.749 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.378 |
|
| \begin{align*}
\left (x^{2} y-1\right ) y^{\prime }+x y^{2}-1&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
3.461 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+y x -3 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.357 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.370 |
|
| \begin{align*}
\left (1+x^{2}+y^{2}\right ) y^{\prime }+2 y x +x^{2}+3&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
1.973 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y+\left (1+\sin \left (x \right )\right ) \cos \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.935 |
|
| \begin{align*}
y^{2}+12 x^{2} y+\left (2 y x +4 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
9.420 |
|
| \begin{align*}
\left (x^{2}-y\right ) y^{\prime }+x&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| \begin{align*}
\left (x^{2}-y\right ) y^{\prime }-4 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.586 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.747 |
|
| \begin{align*}
2 x y y^{\prime }+3 x^{2}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.243 |
|
| \begin{align*}
\left (2 x y^{3}-x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
93.477 |
|
| \begin{align*}
\left (y x -1\right )^{2} x y^{\prime }+\left (1+x^{2} y^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
3.445 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.678 |
|
| \begin{align*}
3 x y^{2} y^{\prime }+y^{3}-2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.097 |
|
| \begin{align*}
2 y^{3} y^{\prime }+x y^{2}-x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.129 |
|
| \begin{align*}
\left (2 x y^{3}+y x +x^{2}\right ) y^{\prime }-y x +y^{2}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
2.177 |
|
| \begin{align*}
\left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.108 |
|
| \begin{align*}
y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.307 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.267 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.378 |
|
| \begin{align*}
6 y^{\prime \prime }-11 y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.266 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.284 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }-6 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.074 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-2 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.058 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-a^{2} y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.057 |
|
| \begin{align*}
y^{\prime \prime }-2 k y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.383 |
|
| \begin{align*}
y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.034 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| \begin{align*}
3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.045 |
|
| \begin{align*}
y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.307 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.042 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-11 y^{\prime \prime }-12 y^{\prime }+36 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.059 |
|
| \begin{align*}
36 y^{\prime \prime \prime \prime }-37 y^{\prime \prime }+4 y^{\prime }+5 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+36 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.084 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.057 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+20 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.311 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.060 |
|
| \begin{align*}
y^{\prime \prime \prime }+8 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.044 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| \begin{align*}
y^{\prime }+2 y^{\prime \prime \prime }+y^{\left (5\right )}&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.065 |
|
| \begin{align*}
y^{\prime \prime }&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+20 y&=0 \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.091 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.360 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=12 \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.387 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{i x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.397 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.534 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-8 y&=9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }&=2 \,{\mathrm e}^{2 x} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{2}+2 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x +\sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.056 |
|
| \begin{align*}
y^{\prime \prime }+y&=4 x \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\sin \left (2 x \right ) x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{-2 x}+x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=x +{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right )+{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.622 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (2 x \right ) \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.892 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 x} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=5 \sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=8 \cos \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= -1 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.738 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \left (2 x -3\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.592 |
|