| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{\prime \prime }+x&=\cos \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\frac {x^{2} {y^{\prime }}^{2}}{2 y}+4 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
3.573 |
|
| \begin{align*}
y^{\prime }+c y&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.353 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+k^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.939 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y^{\prime \prime }+n y \sin \left (x \right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
35.298 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {1-y^{2}}\, \arcsin \left (y\right )}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.196 |
|
| \begin{align*}
v^{\prime \prime }&=\left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
58.293 |
|
| \begin{align*}
v^{\prime }+u^{2} v&=\sin \left (u \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.466 |
|
| \begin{align*}
\sqrt {y^{\prime }+y}&=\left (y^{\prime \prime }+2 x \right )^{{1}/{4}} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
28.725 |
|
| \begin{align*}
v^{\prime }+\frac {2 v}{u}&=3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.716 |
|
| \begin{align*}
\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.520 |
|
| \begin{align*}
y^{\prime }+\sqrt {\frac {1-y^{2}}{-x^{2}+1}}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
10.332 |
|
| \begin{align*}
-y^{\prime } x +y&=b \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.928 |
|
| \begin{align*}
x^{\prime }&=k \left (A -n x\right ) \left (M -m x\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.093 |
|
| \begin{align*}
y^{\prime }&=1+\frac {1}{x}-\frac {1}{y^{2}+2}-\frac {1}{x \left (y^{2}+2\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.048 |
|
| \begin{align*}
y^{2}&=x \left (-x +y\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
18.771 |
|
| \begin{align*}
2 x^{2} y+y^{3}-x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
73.282 |
|
| \begin{align*}
2 a x +b y+\left (2 c y+b x +e \right ) y^{\prime }&=g \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
80.457 |
|
| \begin{align*}
\sec \left (x \right )^{2} \tan \left (y\right ) y^{\prime }+\sec \left (y\right )^{2} \tan \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
31.601 |
|
| \begin{align*}
x +y y^{\prime }&=m y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
32.002 |
|
| \begin{align*}
\frac {2 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
13.184 |
|
| \begin{align*}
\left (T+\frac {1}{\sqrt {t^{2}-T^{2}}}\right ) T^{\prime }&=\frac {T}{t \sqrt {t^{2}-T^{2}}}-t \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
11.266 |
|
| \begin{align*}
y^{\prime }+y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.394 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.140 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\frac {\sin \left (x \right )}{y^{3}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.312 |
|
| \begin{align*}
p^{\prime }&=\frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.757 |
|
| \begin{align*}
\left (T \ln \left (t \right )-1\right ) T&=t T^{\prime } \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.675 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.207 |
|
| \begin{align*}
y-\cos \left (x \right ) y^{\prime }&=y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.939 |
|
| \begin{align*}
x {y^{\prime }}^{2}+2 y^{\prime }-y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.717 |
|
| \begin{align*}
2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.894 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{z -y^{\prime }} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
\sqrt {t^{2}+T}&=T^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
13.154 |
|
| \begin{align*}
{y^{\prime }}^{2} \left (x^{2}-1\right )&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| \begin{align*}
y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.334 |
|
| \begin{align*}
\theta ^{\prime \prime }&=-p^{2} \theta \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.009 |
|
| \begin{align*}
\sec \left (\theta \right )^{2}&=\frac {m s^{\prime }}{k} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {m \sqrt {1+{y^{\prime }}^{2}}}{k} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
7.513 |
|
| \begin{align*}
\phi ^{\prime \prime }&=\frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
62.836 |
|
| \begin{align*}
y^{\prime }&=x \left (a y^{2}+b \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.390 |
|
| \begin{align*}
n^{\prime }&=\left (n^{2}+1\right ) x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.109 |
|
| \begin{align*}
v^{\prime }+\frac {2 v}{u}&=3 v \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.234 |
|
| \begin{align*}
\sqrt {-u^{2}+1}\, v^{\prime }&=2 u \sqrt {1-v^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.242 |
|
| \begin{align*}
\sqrt {1+v^{\prime }}&=\frac {{\mathrm e}^{u}}{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.580 |
|
| \begin{align*}
\frac {y^{\prime }}{x}&=y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.226 |
|
| \begin{align*}
y^{\prime }&=1+\frac {2 y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.553 |
|
| \begin{align*}
v^{\prime }+2 u v&=2 u \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.428 |
|
| \begin{align*}
1+v^{2}+\left (u^{2}+1\right ) v v^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.049 |
|
| \begin{align*}
u \ln \left (u \right ) v^{\prime }+\sin \left (v\right )^{2}&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.682 |
|
| \begin{align*}
\theta ^{\prime \prime }-p^{2} \theta &=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.841 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.520 |
|
| \begin{align*}
y^{\prime \prime }+12 y&=7 y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.201 |
|
| \begin{align*}
r^{\prime \prime }-a^{2} r&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.693 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-a^{4} y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.061 |
|
| \begin{align*}
v^{\prime \prime }-6 v^{\prime }+13 v&={\mathrm e}^{-2 u} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.400 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }-y&=\sin \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
y^{\prime \prime }+3 y&=\sin \left (x \right )+\frac {\sin \left (3 x \right )}{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.352 |
|
| \begin{align*}
5 x^{\prime }+x&=\sin \left (3 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.411 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }-6 x^{\prime \prime \prime }+11 x^{\prime \prime }-6 x^{\prime }&={\mathrm e}^{-3 t} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.167 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+x^{3} y^{\prime \prime \prime }-20 x^{2} y^{\prime \prime }+20 y^{\prime } x&=17 x^{6} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| \begin{align*}
t^{4} x^{\prime \prime \prime \prime }-2 t^{3} x^{\prime \prime \prime }-20 t^{2} x^{\prime \prime }+12 t x^{\prime }+16 x&=\cos \left (3 \ln \left (t \right )\right ) \\
\end{align*} |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.200 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.074 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&={\mathrm e}^{2 x} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.170 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=\cos \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
6.747 |
|
| \begin{align*}
y^{\prime \prime }&=c \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
6.451 |
|
| \begin{align*}
y^{\prime \prime }&=c \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
9.578 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.216 |
|
| \begin{align*}
y^{\prime \prime }&=-m^{2} y \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.884 |
|
| \begin{align*}
1+{y^{\prime }}^{2}+\frac {m y^{\prime \prime }}{\sqrt {1+{y^{\prime }}^{2}}}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
15.571 |
|
| \begin{align*}
y&=y^{\prime } x +y^{\prime }-{y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.787 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }&=y x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
y-2 y^{\prime } x -y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.716 |
|
| \begin{align*}
y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{x \left (x^{2}+1\right )} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.173 |
|
| \begin{align*}
y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x}&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y&=\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
12.870 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=2 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \begin{align*}
v^{\prime \prime }+\frac {2 v^{\prime }}{r}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| \begin{align*}
y^{\prime \prime }-2 y y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.655 |
|
| \begin{align*}
y^{\prime \prime }-{y^{\prime }}^{2}-y {y^{\prime }}^{3}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
0.575 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=r y^{\prime \prime } \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
13.177 |
|
| \begin{align*}
y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5}&=0 \\
\end{align*} |
[[_3rd_order, _missing_y], [_3rd_order, _with_exponential_symmetries], [_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
0.396 |
|
| \begin{align*}
\left (1+y^{2}\right ) y^{\prime \prime }-2 y {y^{\prime }}^{2}-2 \left (1+y^{2}\right ) y^{\prime }&=y^{2} \left (1+y^{2}\right ) \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
142.660 |
|
| \begin{align*}
y^{2} y^{\prime \prime \prime }-\left (3 y y^{\prime }+2 x y^{2}\right ) y^{\prime \prime }+\left (2 {y^{\prime }}^{2}+2 y y^{\prime } x +3 y^{2} x^{2}\right ) y^{\prime }+x^{3} y^{3}&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
0.060 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.755 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
x^{3} v^{\prime \prime \prime }+2 x^{2} v^{\prime \prime }+v&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.211 |
|
| \begin{align*}
v^{\prime \prime }+\frac {2 x v^{\prime }}{x^{2}+1}+\frac {v}{\left (x^{2}+1\right )^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.408 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=-x^{2}+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.130 |
|
| \begin{align*}
y^{\prime }+\cot \left (x \right ) y&=\csc \left (x \right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.611 |
|
| \begin{align*}
y^{\prime }&=x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.812 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+x^{2} y&=x^{3}-x^{2} \arctan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.216 |
|
| \begin{align*}
y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{x \left (x^{2}+1\right )} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.177 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}-1\right ) y&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.128 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.104 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.768 |
|
| \begin{align*}
y^{\prime }+\sin \left (x \right ) y&=\sin \left (x \right ) y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.509 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-y x&=a x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.364 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.921 |
|
| \begin{align*}
3 y^{2} y^{\prime }+y^{3}&=x -1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.051 |
|