| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=\frac {x^{2} y-32}{-x^{2}+16}+2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.822 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.017 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.389 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=a x \\
y \left (0\right ) &= 2 a \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.042 |
|
| \begin{align*}
y^{\prime }&=1-\frac {\sin \left (x +y\right )}{\cos \left (x \right ) \sin \left (y\right )} \\
y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.435 |
|
| \begin{align*}
y^{\prime }&=y^{3} \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
5.044 |
|
| \begin{align*}
y^{\prime }&=\frac {2 \sqrt {-1+y}}{3} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.863 |
|
| \begin{align*}
m v^{\prime }&=m g -k v^{2} \\
v \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
8.292 |
|
| \begin{align*}
y^{\prime }+y&=4 \,{\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.154 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=5 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.111 |
|
| \begin{align*}
x^{2} y^{\prime }-4 y x&=x^{7} \sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| \begin{align*}
y^{\prime }+2 y x&=2 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.112 |
|
| \begin{align*}
y^{\prime }+\frac {2 x y}{-x^{2}+1}&=4 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.119 |
|
| \begin{align*}
y^{\prime }+\frac {2 x y}{x^{2}+1}&=\frac {4}{\left (x^{2}+1\right )^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.104 |
|
| \begin{align*}
2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right )&=4 \cos \left (x \right )^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.167 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x \ln \left (x \right )}&=9 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.168 |
|
| \begin{align*}
y^{\prime }-\tan \left (x \right ) y&=8 \sin \left (x \right )^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \begin{align*}
t x^{\prime }+2 x&=4 \,{\mathrm e}^{t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.139 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right ) \left (y \sec \left (x \right )-2\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.682 |
|
| \begin{align*}
1-\sin \left (x \right ) y-\cos \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.134 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=2 x^{2} \ln \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.141 |
|
| \begin{align*}
y^{\prime }+\alpha y&={\mathrm e}^{\beta x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.153 |
|
| \begin{align*}
y^{\prime }+\frac {m y}{x}&=\ln \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.245 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=4 x \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.228 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=\sin \left (2 x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.878 |
|
| \begin{align*}
x^{\prime }+\frac {2 x}{4-t}&=5 \\
x \left (0\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.600 |
|
| \begin{align*}
y-{\mathrm e}^{x}+y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.050 |
|
| \begin{align*}
y^{\prime }-2 y&=\left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right . \\
y \left (0\right ) &= 3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.611 |
|
| \begin{align*}
y^{\prime }-2 y&=\left \{\begin {array}{cc} 1-x & x <1 \\ 0 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.647 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}&=9 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
3.367 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.169 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{-2 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.895 |
|
| \begin{align*}
y^{\prime }+\cot \left (x \right ) y&=2 \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.466 |
|
| \begin{align*}
-y+y^{\prime } x&=x^{2} \ln \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.232 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.075 |
|
| \begin{align*}
\left (3 x -y\right ) y^{\prime }&=3 y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.378 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x +y\right )^{2}}{2 x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.671 |
|
| \begin{align*}
\sin \left (\frac {y}{x}\right ) \left (-y+y^{\prime } x \right )&=x \cos \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.781 |
|
| \begin{align*}
y^{\prime } x&=\sqrt {16 x^{2}-y^{2}}+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
60.969 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {9 x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.306 |
|
| \begin{align*}
y \left (x^{2}-y^{2}\right )-x \left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| \begin{align*}
y^{\prime } x +y \ln \left (x \right )&=y \ln \left (y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.984 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x -2 x^{2}}{x^{2}-y x +y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.000 |
|
| \begin{align*}
2 y y^{\prime } x -2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.474 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}+3 y x +x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.773 |
|
| \begin{align*}
y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
34.474 |
|
| \begin{align*}
2 x \left (2 x +y\right ) y^{\prime }&=y \left (4 x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
19.424 |
|
| \begin{align*}
y^{\prime } x&=x \tan \left (\frac {y}{x}\right )+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.798 |
|
| \begin{align*}
y^{\prime }&=\frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
50.497 |
|
| \begin{align*}
y^{\prime }&=\frac {-2 x +4 y}{x +y} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
39.998 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -y}{x +4 y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.953 |
|
| \begin{align*}
y^{\prime }&=\frac {y-\sqrt {x^{2}+y^{2}}}{x} \\
y \left (3\right ) &= 4 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
24.100 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {4 x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
61.646 |
|
| \begin{align*}
y^{\prime }&=\frac {x +a y}{a x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
25.559 |
|
| \begin{align*}
y^{\prime }&=\frac {x +\frac {y}{2}}{\frac {x}{2}-y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
27.024 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=\frac {4 x^{2} \cos \left (x \right )}{y} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.939 |
|
| \begin{align*}
y^{\prime }+\frac {\tan \left (x \right ) y}{2}&=2 y^{3} \sin \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.518 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{2 x}&=6 y^{{1}/{3}} x^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.761 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=6 \sqrt {x^{2}+1}\, \sqrt {y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.177 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=6 y^{2} x^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.036 |
|
| \begin{align*}
2 x \left (y^{\prime }+x^{2} y^{3}\right )+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.030 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) \left (y^{\prime }-\sqrt {y}\right )&=2 \left (b -a \right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.428 |
|
| \begin{align*}
y^{\prime }+\frac {6 y}{x}&=\frac {3 y^{{2}/{3}} \cos \left (x \right )}{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.715 |
|
| \begin{align*}
y^{\prime }+4 y x&=4 x^{3} \sqrt {y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.928 |
|
| \begin{align*}
y^{\prime }-\frac {y}{2 x \ln \left (x \right )}&=2 x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.427 |
|
| \begin{align*}
y^{\prime }-\frac {y}{\left (\pi -1\right ) x}&=\frac {3 x y^{\pi }}{1-\pi } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.487 |
|
| \begin{align*}
2 y^{\prime }+\cot \left (x \right ) y&=\frac {8 \cos \left (x \right )^{3}}{y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
83.427 |
|
| \begin{align*}
\left (1-\sqrt {3}\right ) y^{\prime }+y \sec \left (x \right )&=y^{\sqrt {3}} \sec \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.065 |
|
| \begin{align*}
y^{\prime }+\frac {2 x y}{x^{2}+1}&=x y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.212 |
|
| \begin{align*}
y^{\prime }+\cot \left (x \right ) y&=y^{3} \sin \left (x \right )^{3} \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.069 |
|
| \begin{align*}
y^{\prime }&=\left (9 x -y\right )^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.852 |
|
| \begin{align*}
y^{\prime }&=\left (4 x +y+2\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
9.242 |
|
| \begin{align*}
y^{\prime }&=\sin \left (3 x -3 y+1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.220 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (\ln \left (y x \right )-1\right )}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
7.117 |
|
| \begin{align*}
y^{\prime }&=2 x \left (x +y\right )^{2}-1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.546 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y-1}{2 x -y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
36.567 |
|
| \begin{align*}
y^{\prime }+p \left (x \right ) y+q \left (x \right ) y^{2}&=r \left (x \right ) \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
✗ |
11.171 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}-y^{2}&=-\frac {2}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
16.874 |
|
| \begin{align*}
y^{\prime }+\frac {7 y}{x}-3 y^{2}&=\frac {3}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.322 |
|
| \begin{align*}
\frac {y^{\prime }}{y}+p \left (x \right ) \ln \left (y\right )&=q \left (x \right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.658 |
|
| \begin{align*}
\frac {y^{\prime }}{y}-\frac {2 \ln \left (y\right )}{x}&=\frac {1-2 \ln \left (x \right )}{x} \\
y \left (1\right ) &= {\mathrm e} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.917 |
|
| \begin{align*}
\sec \left (y\right )^{2} y^{\prime }+\frac {\tan \left (y\right )}{2 \sqrt {x +1}}&=\frac {1}{2 \sqrt {x +1}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
86.557 |
|
| \begin{align*}
y \,{\mathrm e}^{y x}+\left (2 y-x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
✗ |
3.791 |
|
| \begin{align*}
\cos \left (y x \right )-x y \sin \left (y x \right )-x^{2} \sin \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
✓ |
✓ |
✓ |
0.311 |
|
| \begin{align*}
y+3 x^{2}+y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| \begin{align*}
2 x \,{\mathrm e}^{y}+\left (3 y^{2}+x^{2} {\mathrm e}^{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.121 |
|
| \begin{align*}
y^{2}-2 x +2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.623 |
|
| \begin{align*}
4 \,{\mathrm e}^{2 x}+2 y x -y^{2}+\left (x -y\right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.188 |
|
| \begin{align*}
\frac {1}{x}-\frac {y}{x^{2}+y^{2}}+\frac {x y^{\prime }}{x^{2}+y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| \begin{align*}
y \cos \left (y x \right )-\sin \left (x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.229 |
|
| \begin{align*}
2 y^{2} {\mathrm e}^{2 x}+3 x^{2}+2 y \,{\mathrm e}^{2 x} y^{\prime }&=0 \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| \begin{align*}
y^{2}+\cos \left (x \right )+\left (2 y x +\sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
0.204 |
|
| \begin{align*}
\sin \left (y\right )+\cos \left (x \right ) y+\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
0.300 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.566 |
|
| \begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.359 |
|
| \begin{align*}
y^{\prime \prime }-36 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.676 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.586 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.073 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.080 |
|