| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{4 x^{2}}\right ) y&=x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
7.658 |
|
| \begin{align*}
y^{\prime \prime }+y&=f \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.866 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (x -\frac {1}{2}\right ) y^{\prime }+\frac {y}{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
7.488 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
7.282 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (-5 x +1\right ) y^{\prime }-4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Jacobi] |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \begin{align*}
\left (x^{2}-1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
y^{\prime \prime } x +4 y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (x +1\right ) y^{\prime }-k y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| \begin{align*}
x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✗ |
✓ |
✗ |
0.095 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
✗ |
✓ |
✗ |
0.151 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.621 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.698 |
|
| \begin{align*}
y^{\prime \prime }-x^{2} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
1.385 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.026 |
|
| \begin{align*}
y^{\prime \prime } x +x^{2} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| \begin{align*}
y^{\prime \prime }+\alpha ^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.858 |
|
| \begin{align*}
y^{\prime \prime }-\alpha ^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.006 |
|
| \begin{align*}
y^{\prime \prime }+\beta y^{\prime }+\gamma y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
12.412 |
|
| \begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✗ |
✓ |
✓ |
✗ |
87.602 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-\nu ^{2}+x^{2}\right ) y&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.855 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=18 t \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.180 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=f \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} t & 0\le t \le 3 \\ t +2 & 3<t \end {array}\right . \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.346 |
|
| \begin{align*}
x^{\prime }+y^{\prime }+x&=0 \\
x^{\prime }-x+2 y^{\prime }&={\mathrm e}^{-t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.189 |
|
| \begin{align*}
x^{\prime \prime }+2 t x^{\prime }-4 x&=1 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[_erf] |
✓ |
✓ |
✓ |
✗ |
0.300 |
|
| \begin{align*}
c v^{\prime \prime }+\frac {v^{\prime }}{r}+\frac {v}{L}&=-\delta \left (t \right )+\delta \left (t -1\right ) \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.372 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.200 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.079 |
|
| \begin{align*}
x y \left (1-{y^{\prime }}^{2}\right )&=\left (-y^{2}-a^{2}+x^{2}\right ) y^{\prime } \\
\end{align*} |
[_rational] |
✓ |
✗ |
✓ |
✗ |
152.501 |
|
| \begin{align*}
y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x}&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.269 |
|
| \begin{align*}
y^{\prime \prime }-2 k y^{\prime }+k^{2} y&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
19.350 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -a^{2} y&=0 \\
\end{align*} |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
36.086 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
10.927 |
|
| \begin{align*}
-y^{\prime } x +y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.728 |
|
| \begin{align*}
\left (1+u \right ) v+\left (1-v\right ) u v^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.403 |
|
| \begin{align*}
1+y-\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.017 |
|
| \begin{align*}
\left (t^{2}+t^{2} x\right ) x^{\prime }+x^{2}+t x^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.333 |
|
| \begin{align*}
y-a +x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.875 |
|
| \begin{align*}
z-\left (-a^{2}+t^{2}\right ) z^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.555 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.514 |
|
| \begin{align*}
1+s^{2}-\sqrt {t}\, s^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.753 |
|
| \begin{align*}
r^{\prime }+r \tan \left (t \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.759 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }-\sqrt {1-y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.028 |
|
| \begin{align*}
y^{\prime } \sqrt {-x^{2}+1}-\sqrt {1-y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.876 |
|
| \begin{align*}
3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.145 |
|
| \begin{align*}
x -x y^{2}+\left (y-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.342 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.463 |
|
| \begin{align*}
y^{\prime } x +x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.693 |
|
| \begin{align*}
x +y+\left (-x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.154 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.104 |
|
| \begin{align*}
\left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.854 |
|
| \begin{align*}
2 \sqrt {t s}-s+t s^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.100 |
|
| \begin{align*}
t -s+t s^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.170 |
|
| \begin{align*}
y^{\prime } y^{2} x&=x^{3}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.064 |
|
| \begin{align*}
x \cos \left (\frac {y}{x}\right ) \left (y^{\prime } x +y\right )&=y \sin \left (\frac {y}{x}\right ) \left (-y+y^{\prime } x \right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
8.917 |
|
| \begin{align*}
3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
67.798 |
|
| \begin{align*}
x +2 y+1-\left (3+2 x +4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.313 |
|
| \begin{align*}
x +2 y+1-\left (2 x -3\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.081 |
|
| \begin{align*}
\frac {-y^{\prime } x +y}{\sqrt {x^{2}+y^{2}}}&=m \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
25.277 |
|
| \begin{align*}
\frac {y y^{\prime }+x}{\sqrt {x^{2}+y^{2}}}&=m \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
59.599 |
|
| \begin{align*}
y+\frac {x}{y^{\prime }}&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.674 |
|
| \begin{align*}
y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.945 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x +1}&=\left (x +1\right )^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.538 |
|
| \begin{align*}
y^{\prime }-\frac {a y}{x}&=\frac {x +1}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.827 |
|
| \begin{align*}
\left (-x^{2}+x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y-a \,x^{3}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.026 |
|
| \begin{align*}
s^{\prime } \cos \left (t \right )+s \sin \left (t \right )&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.194 |
|
| \begin{align*}
s^{\prime }+s \cos \left (t \right )&=\frac {\sin \left (2 t \right )}{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.421 |
|
| \begin{align*}
y^{\prime }-\frac {n y}{x}&={\mathrm e}^{x} x^{n} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.091 |
|
| \begin{align*}
y^{\prime }+\frac {n y}{x}&=a \,x^{-n} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
1.407 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.022 |
|
| \begin{align*}
y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}-1&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.284 |
|
| \begin{align*}
y^{\prime }+y x&=x^{3} y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.908 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-y x +a x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.759 |
|
| \begin{align*}
3 y^{2} y^{\prime }-a y^{3}-x -1&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.007 |
|
| \begin{align*}
\left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
1.888 |
|
| \begin{align*}
y^{\prime } x&=\left (y \ln \left (x \right )-2\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.129 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
5.790 |
|
| \begin{align*}
x^{2}+y+\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
1.649 |
|
| \begin{align*}
y-3 x^{2}-\left (4 y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
1.680 |
|
| \begin{align*}
\left (y^{3}-x \right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✓ |
4.098 |
|
| \begin{align*}
\frac {y^{2}}{\left (x -y\right )^{2}}-\frac {1}{x}+\left (\frac {1}{y}-\frac {x^{2}}{\left (x -y\right )^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.764 |
|
| \begin{align*}
6 x y^{2}+4 x^{3}+3 \left (2 x^{2} y+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
1.934 |
|
| \begin{align*}
\frac {x}{\left (x +y\right )^{2}}+\frac {\left (2 x +y\right ) y^{\prime }}{\left (x +y\right )^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.556 |
|
| \begin{align*}
\frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}}&=\frac {2 y y^{\prime }}{x^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.622 |
|
| \begin{align*}
\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.082 |
|
| \begin{align*}
y y^{\prime }+x&=\frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.543 |
|
| \begin{align*}
y&=2 y^{\prime } x +{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.412 |
|
| \begin{align*}
y&=x {y^{\prime }}^{2}+{y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| \begin{align*}
y&=x \left (1+y^{\prime }\right )+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| \begin{align*}
y&=y {y^{\prime }}^{2}+2 y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.210 |
|
| \begin{align*}
y&=y y^{\prime }+y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.175 |
|
| \begin{align*}
y&=y^{\prime } x +\sqrt {1-{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.714 |
|
| \begin{align*}
y&=y^{\prime } x +y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.072 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {1}{y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.573 |
|
| \begin{align*}
y&=y^{\prime } x -\frac {1}{{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.716 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x}-\sqrt {3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.457 |
|
| \begin{align*}
2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {1}{2 y^{\prime }} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
4.039 |
|
| \begin{align*}
x y^{\prime \prime \prime }&=2 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.200 |
|