| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=2 x +1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.566 |
|
| \begin{align*}
y^{\prime }&=\left (x -2\right )^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x} \\
y \left (4\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}} \\
y \left (1\right ) &= 5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\sqrt {x +2}} \\
y \left (2\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {x^{2}+9} \\
y \left (-4\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.837 |
|
| \begin{align*}
y^{\prime }&=\frac {10}{x^{2}+1} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.458 |
|
| \begin{align*}
y^{\prime }&=\cos \left (2 x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\sqrt {-x^{2}+1}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{-x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \begin{align*}
y^{\prime }&=2 x +1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.476 |
|
| \begin{align*}
y^{\prime }&=\left (x -2\right )^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x} \\
y \left (4\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}} \\
y \left (1\right ) &= 5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\sqrt {x +2}} \\
y \left (2\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {x^{2}+9} \\
y \left (-4\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.746 |
|
| \begin{align*}
y^{\prime }&=\frac {10}{x^{2}+1} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| \begin{align*}
y^{\prime }&=\cos \left (2 x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\sqrt {-x^{2}+1}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{-x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.479 |
|
| \begin{align*}
y^{\prime }&=-x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| \begin{align*}
y^{\prime }&=-x \sin \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
y^{\prime }&=x \ln \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
y^{\prime }&=-x \,{\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
y^{\prime }&=x \sin \left (x^{2}\right ) \\
y \left (\frac {\sqrt {2}\, \sqrt {\pi }}{2}\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| \begin{align*}
y^{\prime }&=\tan \left (x \right ) \\
y \left (\frac {\pi }{4}\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.996 |
|
| \begin{align*}
x^{\prime }&=1-\sin \left (2 t \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| \begin{align*}
y^{\prime }&=2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| \begin{align*}
y^{\prime }&=2 \,{\mathrm e}^{3 x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.399 |
|
| \begin{align*}
y^{\prime }&=\frac {2}{\sqrt {-x^{2}+1}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.462 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| \begin{align*}
y^{\prime }&=\arcsin \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| \begin{align*}
y^{\prime }&=t^{2}+3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 t} t \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
y^{\prime }&=\sin \left (3 t \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t \right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{t^{2}+4} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
y^{\prime }&=\ln \left (t \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{\sqrt {t}+1} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 t} t \\
y \left (1\right ) &= 5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t \right )^{2} \\
y \left (\frac {\pi }{6}\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| \begin{align*}
y^{\prime }&=8 \,{\mathrm e}^{4 t}+t \\
y \left (0\right ) &= 12 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \begin{align*}
y^{\prime }+\frac {m}{x}&=\ln \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{{2}/{3}}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| \begin{align*}
y^{\prime }&=x^{2} \ln \left (x \right ) \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.377 |
|
| \begin{align*}
y^{\prime }&=1-x^{5}+\sqrt {x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.419 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x} \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.895 |
|
| \begin{align*}
y^{\prime }&=x +\frac {1}{x} \\
y \left (-2\right ) &= 5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| \begin{align*}
\left (x^{3}+1\right ) y^{\prime }&=3 \tan \left (x \right ) x^{2} \\
y \left (0\right ) &= \frac {\pi }{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| \begin{align*}
x&=y^{\prime } \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
181.111 |
|
| \begin{align*}
y^{\prime } \left (x -\ln \left (y^{\prime }\right )\right )&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.480 |
|
| \begin{align*}
y^{\prime }&=a f \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {a^{2}-x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.049 |
|
| \begin{align*}
x y^{\prime }&=-\sqrt {a^{2}-x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.895 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.581 |
|
| \begin{align*}
y^{\prime } \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (2 x +1\right ) y^{\prime }-x \left (1-x \right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.496 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.253 |
|
| \begin{align*}
{y^{\prime }}^{2} x&=\left (-x +a \right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.095 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x&=\left (a -3 x \right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.103 |
|
| \begin{align*}
4 x \left (-x +a \right ) \left (-x +b \right ) {y^{\prime }}^{2}&=\left (a b -2 x \left (a +b \right )+2 x^{2}\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.977 |
|
| \begin{align*}
x^{2} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
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✓ |
5.805 |
|
| \begin{align*}
{y^{\prime }}^{3}-a x y^{\prime }+x^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.629 |
|
| \begin{align*}
{y^{\prime }}^{3}+\left (-3 x +1\right ) {y^{\prime }}^{2}-x \left (-3 x +1\right ) y^{\prime }-1-x^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.941 |
|
| \begin{align*}
\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime }&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
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✓ |
21.381 |
|
| \begin{align*}
a \cos \left (y^{\prime }\right )+b y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.504 |
|
| \begin{align*}
\sin \left (y^{\prime }\right )+y^{\prime }&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.468 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) \left (\arctan \left (y^{\prime }\right )+a x \right )+y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
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✗ |
2.556 |
|
| \begin{align*}
\ln \left (y^{\prime }\right )+x y^{\prime }+a&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.937 |
|
| \begin{align*}
x&=\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
23.694 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| \begin{align*}
x y^{\prime }&=x^{2}+2 x -3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| \begin{align*}
x^{2} y^{\prime }&=x^{3} \sin \left (3 x \right )+4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \begin{align*}
1-\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.238 |
|
| \begin{align*}
{y^{\prime }}^{2} x -4 y^{\prime }-12 x^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.303 |
|
| \begin{align*}
x y^{\prime }&=2 x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| \begin{align*}
y^{\prime }&=2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| \begin{align*}
y^{\prime }&=x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.529 |
|
| \begin{align*}
y^{\prime }&=x \\
y \left (0\right ) &= -3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| \begin{align*}
y^{\prime }&=\sin \left (5 x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
y^{\prime }&=\left (x +1\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \begin{align*}
1+{\mathrm e}^{3 x} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
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✓ |
0.543 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{1+\sin \left (x \right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
x^{\prime }+t&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3 x}+\sin \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| \begin{align*}
y^{\prime }&=2 x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.580 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3 x}-x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=\arctan \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| \begin{align*}
x y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| \begin{align*}
y^{\prime }&=\arcsin \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \begin{align*}
\left (x^{3}+1\right ) y^{\prime }&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| \begin{align*}
\left (x^{2}-3 x +2\right ) y^{\prime }&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
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✓ |
0.665 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \begin{align*}
y^{\prime }&=2 \sin \left (x \right ) \cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| \begin{align*}
y^{\prime }&=\ln \left (x \right ) \\
y \left ({\mathrm e}\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }&=1 \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| \begin{align*}
x \left (x^{2}-4\right ) y^{\prime }&=1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| \begin{align*}
\left (x +1\right ) \left (x^{2}+1\right ) y^{\prime }&=2 x^{2}+x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| \begin{align*}
y^{\prime }&=x +1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
y^{\prime }&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.372 |
|
| \begin{align*}
y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| \begin{align*}
y^{\prime }&=1+\frac {\sec \left (x \right )}{x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.683 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \begin{align*}
x y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| \begin{align*}
\frac {y^{\prime }}{x}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.340 |
|
| \begin{align*}
y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.374 |
|
| \begin{align*}
y^{\prime }&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \begin{align*}
y^{\prime }&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| \begin{align*}
y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| \begin{align*}
y^{\prime }&=a x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| \begin{align*}
c y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
c y^{\prime }&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.862 |
|
| \begin{align*}
c y^{\prime }&=a x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.823 |
|
| \begin{align*}
x y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
5 y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.403 |
|
| \begin{align*}
{\mathrm e} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \begin{align*}
\pi y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.476 |
|
| \begin{align*}
f \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| \begin{align*}
x y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| \begin{align*}
x y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
x \sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
x \sin \left (x \right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| \begin{align*}
{y^{\prime }}^{n}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.511 |
|
| \begin{align*}
x {y^{\prime }}^{n}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.576 |
|
| \begin{align*}
y^{\prime }-\frac {1}{\sqrt {\operatorname {a4} \,x^{4}+\operatorname {a3} \,x^{3}+\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0}}}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| \begin{align*}
x y^{\prime }-\sqrt {a^{2}-x^{2}}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| \begin{align*}
{y^{\prime }}^{2}+a x y^{\prime }-b \,x^{2}-c&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
32.555 |
|
| \begin{align*}
y^{\prime }-1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.732 |
|
| \begin{align*}
x^{2} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.439 |
|
| \begin{align*}
{y^{\prime }}^{3}-a x y^{\prime }+x^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.532 |
|
| \begin{align*}
\sin \left (y^{\prime }\right )+y^{\prime }-x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.298 |
|
| \begin{align*}
a \cos \left (y^{\prime }\right )+b y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.311 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) \left (\arctan \left (y^{\prime }\right )+a x \right )+y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.288 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.245 |
|
| \begin{align*}
x^{\prime }&=t \cos \left (t^{2}\right ) \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.329 |
|
| \begin{align*}
x^{\prime }&=\frac {t +1}{\sqrt {t}} \\
x \left (1\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.965 |
|
| \begin{align*}
x^{\prime }&=t \,{\mathrm e}^{-2 t} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \begin{align*}
x^{\prime }&=\frac {1}{t \ln \left (t \right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.862 |
|
| \begin{align*}
\sqrt {t}\, x^{\prime }&=\cos \left (\sqrt {t}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| \begin{align*}
x^{\prime }&=\frac {{\mathrm e}^{-t}}{\sqrt {t}} \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.153 |
|
| \begin{align*}
x^{\prime }&=\sin \left (t \right )+\cos \left (t \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.654 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}-1} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| \begin{align*}
u^{\prime }&=4 t \ln \left (t \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.940 |
|
| \begin{align*}
z^{\prime }&={\mathrm e}^{-2 x} x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.623 |
|
| \begin{align*}
T^{\prime }&={\mathrm e}^{-t} \sin \left (2 t \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.884 |
|
| \begin{align*}
x^{\prime }&=\sec \left (t \right )^{2} \\
x \left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.391 |
|
| \begin{align*}
y^{\prime }&=x -\frac {1}{3} x^{3} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.886 |
|
| \begin{align*}
x^{\prime }&=2 \sin \left (t \right )^{2} \\
x \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.890 |
|
| \begin{align*}
x V^{\prime }&=x^{2}+1 \\
V \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| \begin{align*}
x y^{\prime }-\sin \left (x \right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| \begin{align*}
y^{\prime }&=1-x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \begin{align*}
y^{\prime }&=x -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| \begin{align*}
y^{\prime }&=x^{2}+{\mathrm e}^{x}-\sin \left (x \right ) \\
y \left (2\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| \begin{align*}
y^{\prime }&=1+3 x \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| \begin{align*}
y^{\prime }&=x +\frac {1}{x} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.862 |
|
| \begin{align*}
y^{\prime }&=2 \sin \left (x \right ) \\
y \left (\pi \right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| \begin{align*}
y^{\prime }&=x \sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.856 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x -1} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x -1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.820 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}-1} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}-1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| \begin{align*}
y^{\prime }&=\tan \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.704 |
|
| \begin{align*}
y^{\prime }&=\tan \left (x \right ) \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.201 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x -1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| \begin{align*}
y^{\prime }&=t^{2}+t \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.400 |
|
| \begin{align*}
y^{\prime }&=t^{2}+1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
y^{\prime }&=-t^{2}+2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.400 |
|
| \begin{align*}
y^{\prime }&=t^{2}-2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \begin{align*}
\theta ^{\prime }&=2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
y^{\prime }&=t^{2} \left (t^{2}+1\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
y^{\prime }&=3-\sin \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.376 |
|
| \begin{align*}
x y^{\prime }&=\arcsin \left (x^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.668 |
|
| \begin{align*}
y^{\prime }&=4 x^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| \begin{align*}
y^{\prime }&=20 \,{\mathrm e}^{-4 x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| \begin{align*}
x y^{\prime }+\sqrt {x}&=2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
\sqrt {x +4}\, y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \begin{align*}
y^{\prime }&=x \cos \left (x^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
y^{\prime }&=x \cos \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| \begin{align*}
x&=\left (x^{2}-9\right ) y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \begin{align*}
1&=\left (x^{2}-9\right ) y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.578 |
|
| \begin{align*}
1&=x^{2}-9 y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \begin{align*}
y^{\prime }&=40 x \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
\left (6+x \right )^{{1}/{3}} y^{\prime }&=1 \\
y \left (2\right ) &= 10 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| \begin{align*}
y^{\prime }&=\frac {x -1}{x +1} \\
y \left (0\right ) &= 8 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
x y^{\prime }+2&=\sqrt {x} \\
y \left (1\right ) &= 6 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }-\sin \left (x \right )&=0 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.154 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.472 |
|
| \begin{align*}
y^{\prime }&=\sin \left (\frac {x}{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
y^{\prime }&=\sin \left (\frac {x}{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
y^{\prime }&=\sin \left (\frac {x}{2}\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.434 |
|
| \begin{align*}
y^{\prime }&=3 \sqrt {x +3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.334 |
|
| \begin{align*}
y^{\prime }&=3 \sqrt {x +3} \\
y \left (1\right ) &= 16 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.506 |
|
| \begin{align*}
y^{\prime }&=3 \sqrt {x +3} \\
y \left (1\right ) &= 20 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.500 |
|
| \begin{align*}
y^{\prime }&=3 \sqrt {x +3} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{-x^{2}} \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{\sqrt {x^{2}+5}} \\
y \left (2\right ) &= 7 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}+1} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-9 x^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
75.109 |
|
| \begin{align*}
x y^{\prime }&=\sin \left (x \right ) \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| \begin{align*}
x y^{\prime }&=\sin \left (x^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.657 |
|
| \begin{align*}
y^{\prime }&=\left \{\begin {array}{cc} 0 & x <0 \\ 1 & 0\le x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.242 |
|
| \begin{align*}
y^{\prime }&=\left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.233 |
|
| \begin{align*}
y^{\prime }&=\left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x <2 \\ 0 & 2\le x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.254 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x^{2}+1} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \begin{align*}
y^{\prime }-{\mathrm e}^{2 x}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \begin{align*}
x^{2} y^{\prime }-\sqrt {x}&=3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
\left (x^{2}-4\right ) y^{\prime }&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| \begin{align*}
\sin \left (x \right )+2 \cos \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.755 |
|
| \begin{align*}
\left (x +2\right ) y^{\prime }-x^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \begin{align*}
y^{\prime }+2 x&=\sin \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
2 x -1-y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \begin{align*}
y^{\prime }&=\left (x^{2}-1\right ) \left (x^{3}-3 x \right )^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
y^{\prime }&=x \sin \left (x^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x \ln \left (x \right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| \begin{align*}
y^{\prime }&=x \ln \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{-x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.389 |
|
| \begin{align*}
y^{\prime }&=\frac {-10-2 x}{\left (x +2\right ) \left (x -4\right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
y^{\prime }&=\frac {-x^{2}+x}{\left (x +1\right ) \left (x^{2}+1\right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {x^{2}-16}}{x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| \begin{align*}
y^{\prime }&=\left (-x^{2}+4\right )^{{3}/{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}-16} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right ) \cot \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.969 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right )^{3} \tan \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.888 |
|
| \begin{align*}
y^{\prime }&=4 x^{3}-x +2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \begin{align*}
y^{\prime }&=\sin \left (2 t \right )-\cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.645 |
|
| \begin{align*}
y^{\prime }&=\frac {\cos \left (\frac {1}{x}\right )}{x^{2}} \\
y \left (\frac {2}{\pi }\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \begin{align*}
y^{\prime }&=\frac {\ln \left (x \right )}{x} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right )^{4} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.818 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{-x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \begin{align*}
y^{\prime }&=x^{2} \sin \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x^{2}-x +1}{\left (x -1\right ) \left (x^{2}+1\right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{\sqrt {x^{2}-1}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right ) \cos \left (x \right )^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.534 |
|
| \begin{align*}
y^{\prime }&=\frac {4 x -9}{3 \left (x -3\right )^{{2}/{3}}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{t^{2}+1} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \begin{align*}
y^{\prime }&=x^{3} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.527 |
|
| \begin{align*}
y^{\prime }&=\cos \left (t \right ) \\
y \left (\frac {\pi }{2}\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \begin{align*}
\sin \left (y \right )^{2}&=x^{\prime } \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
y^{\prime }&=t \sin \left (t^{2}\right ) \\
y \left (\sqrt {\pi }\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.980 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}+1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.463 |
|
| \begin{align*}
3 t^{2}-y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| \begin{align*}
y^{\prime }&=x +1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.426 |
|
| \begin{align*}
y^{\prime }&=1-x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| \begin{align*}
\cos \left (y^{\prime }\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.408 |
|
| \begin{align*}
{\mathrm e}^{y^{\prime }}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| \begin{align*}
\sin \left (y^{\prime }\right )&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| \begin{align*}
\ln \left (y^{\prime }\right )&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.171 |
|
| \begin{align*}
\tan \left (y^{\prime }\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| \begin{align*}
{\mathrm e}^{y^{\prime }}&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| \begin{align*}
\tan \left (y^{\prime }\right )&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| \begin{align*}
x&=\ln \left (y^{\prime }\right )+\sin \left (y^{\prime }\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
9.419 |
|
| \begin{align*}
x&=\sin \left (y^{\prime }\right )+y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.372 |
|
| \begin{align*}
x^{2}+x y^{\prime }&=3 x +y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \begin{align*}
x y^{\prime }&=-\frac {1}{\ln \left (x \right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| \begin{align*}
y^{\prime }&=2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \begin{align*}
y^{\prime }&=-x^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
y^{\prime }&=2 x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3 x}-x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \begin{align*}
x y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.422 |
|
| \begin{align*}
y^{\prime }&=\arcsin \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \begin{align*}
\left (x^{3}+1\right ) y^{\prime }&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=\arctan \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.784 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| \begin{align*}
y^{\prime }&=2 \sin \left (x \right ) \cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \begin{align*}
y^{\prime }&=\ln \left (x \right ) \\
y \left ({\mathrm e}\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }&=1 \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \begin{align*}
x \left (x^{2}-4\right ) y^{\prime }&=1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.837 |
|
| \begin{align*}
\left (x +1\right ) \left (x^{2}+1\right ) y^{\prime }&=2 x^{2}+x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.157 |
|
| \begin{align*}
x y^{\prime }&=2 x^{2}+1 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x} \cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| \begin{align*}
x^{\prime }&=3 t^{2}+4 t \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \begin{align*}
x^{\prime }&=b \,{\mathrm e}^{t} \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
x^{\prime }&=\frac {1}{t^{2}+1} \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
x^{\prime }&=\frac {1}{\sqrt {t^{2}+1}} \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \begin{align*}
x^{\prime }&=\cos \left (t \right ) \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.517 |
|
| \begin{align*}
x^{\prime }&=\frac {\cos \left (t \right )}{\sin \left (t \right )} \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.165 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{z -y^{\prime }} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| \begin{align*}
\sec \left (\theta \right )^{2}&=\frac {m s^{\prime }}{k} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
\sqrt {1+v^{\prime }}&=\frac {{\mathrm e}^{u}}{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
{y^{\prime }}^{2} x -\left (x -a \right )^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.337 |
|
| \begin{align*}
4 x \left (x -1\right ) \left (x -2\right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.139 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.049 |
|
| \begin{align*}
x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| \begin{align*}
4 x \left (x -1\right ) \left (x -2\right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.453 |
|
| \begin{align*}
\left (8 {y^{\prime }}^{3}-27\right ) x&=\frac {12 {y^{\prime }}^{2}}{x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
53.995 |
|
| \begin{align*}
{y^{\prime }}^{2} x -\left (x -a \right )^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.688 |
|
| \begin{align*}
y^{\prime }&=\tan \left (x -\frac {y^{\prime }}{1+{y^{\prime }}^{2}}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
1.303 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x&=\left (3 x -a \right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.270 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x \left (x -a \right ) \left (x -b \right )&=\left (3 x^{2}-2 x \left (a +b \right )+a b \right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.660 |
|
| \begin{align*}
\sqrt {x}\, y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.099 |
|
| \begin{align*}
y^{\prime }&=2 x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.314 |
|
| \begin{align*}
\frac {\ln \left (1+{y^{\prime }}^{2}\right )}{2}-\ln \left (y^{\prime }\right )-x +2&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.217 |
|
| \begin{align*}
x^{3} y^{\prime }-x^{3}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.655 |
|
| \begin{align*}
y^{\prime }&=5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.378 |
|
| \begin{align*}
\frac {1}{x}+y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
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0.422 |
|
| \begin{align*}
y^{\prime }&=3 \sin \left (x \right ) \\
y \left (\pi \right ) &= -1 \\
\end{align*} |
[_quadrature] |
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0.727 |
|
| \begin{align*}
x^{\prime }&=4 \,{\mathrm e}^{-t}-2 \\
x \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
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0.672 |
|
| \begin{align*}
s^{\prime }&=9 \sqrt {u} \\
s \left (4\right ) &= 16 \\
\end{align*} |
[_quadrature] |
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1.663 |
|
| \begin{align*}
y^{\prime }&=-\frac {4}{x^{2}} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_quadrature] |
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1.351 |
|
| \begin{align*}
y^{\prime }&=2 x \\
\end{align*} |
[_quadrature] |
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2.109 |
|
| \begin{align*}
\left (x^{2}+x \right ) y^{\prime }+2 x +1+2 \cos \left (x \right )&=0 \\
\end{align*} |
[_quadrature] |
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1.118 |
|
| \begin{align*}
y^{\prime }+2 x&=2 \\
\end{align*} |
[_quadrature] |
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0.536 |
|
| \begin{align*}
r^{\prime }&=-a \sin \left (\theta \right ) \\
r \left (0\right ) &= 2 a \\
\end{align*} |
[_quadrature] |
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0.281 |
|
| \begin{align*}
\sin \left (\theta \right )^{2} r^{\prime }&=-b \cos \left (\theta \right ) \\
\end{align*} |
[_quadrature] |
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0.384 |
|
| \begin{align*}
r^{\prime }&=0 \\
r \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
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0.359 |
|
| \begin{align*}
r^{\prime }&=c \\
r \left (0\right ) &= a \\
\end{align*} |
[_quadrature] |
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0.605 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 x} \\
\end{align*} |
[_quadrature] |
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0.411 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{t^{2}} \\
\end{align*} |
[_quadrature] |
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0.727 |
|
| \begin{align*}
y^{\prime }&=\cos \left (t \right )^{2} \\
\end{align*} |
[_quadrature] |
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0.414 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{t^{2}-1} \\
\end{align*} |
[_quadrature] |
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0.476 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{t} t \\
\end{align*} |
[_quadrature] |
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0.394 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\sqrt {t^{2}+2 t}} \\
\end{align*} |
[_quadrature] |
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0.540 |
|
| \begin{align*}
y^{\prime }&=t \ln \left (t \right ) \\
\end{align*} |
[_quadrature] |
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0.413 |
|
| \begin{align*}
y^{\prime }&=\frac {t^{2}+1}{t \left (t -2\right )} \\
\end{align*} |
[_quadrature] |
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0.501 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\sqrt {-x^{2}+1}} \\
\end{align*} |
[_quadrature] |
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0.411 |
|
| \begin{align*}
x -\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
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0.642 |
|
| \begin{align*}
x +\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
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0.477 |
|
| \begin{align*}
a^{2}-x y^{\prime } \sqrt {-a^{2}+x^{2}}&=0 \\
\end{align*} |
[_quadrature] |
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1.067 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b x \\
\end{align*} |
[_quadrature] |
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0.475 |
|
| \begin{align*}
y^{\prime }&=t +3 \\
\end{align*} |
[_quadrature] |
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0.394 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 t}-1 \\
\end{align*} |
[_quadrature] |
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0.401 |
|
| \begin{align*}
y^{\prime }&=t \,{\mathrm e}^{-t} \\
\end{align*} |
[_quadrature] |
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0.425 |
|
| \begin{align*}
y^{\prime }&=\frac {t +1}{t} \\
\end{align*} |
[_quadrature] |
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0.480 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 t}-1 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
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0.505 |
|
| \begin{align*}
y^{\prime }&=t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
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0.518 |
|
| \begin{align*}
y^{\prime }&=t \\
\end{align*} |
[_quadrature] |
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1.442 |
|
| \begin{align*}
y^{\prime }&=t^{2}+1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
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0.559 |
|
| \begin{align*}
y^{\prime }&=5 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
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1.761 |
|
| \begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -T \right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
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1.260 |
|
| \begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (t -2\right )+\operatorname {Heaviside}\left (-3+t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
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0.911 |
|
| \begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -1\right )+\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
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0.793 |
|
| \begin{align*}
y^{\prime }&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\
\end{align*} |
[_quadrature] |
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0.398 |
|
| \begin{align*}
y^{\prime }&=2 \,{\mathrm e}^{2 t}-4 \,{\mathrm e}^{t} \\
\end{align*} |
[_quadrature] |
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0.516 |
|
| \begin{align*}
y^{\prime }&=x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
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10.871 |
|
| \begin{align*}
y^{\prime }&=x \\
y \left (0\right ) &= -3 \\
\end{align*} |
[_quadrature] |
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0.940 |
|
| \begin{align*}
y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
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0.641 |
|
| \begin{align*}
y^{\prime }&=\sin \left (5 x \right ) \\
\end{align*} |
[_quadrature] |
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0.485 |
|
| \begin{align*}
y^{\prime }&=\left (x +1\right )^{2} \\
\end{align*} |
[_quadrature] |
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0.473 |
|
| \begin{align*}
1+{\mathrm e}^{3 x} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
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0.658 |
|
| \begin{align*}
y^{\prime }&=2 x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
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2.103 |
|
| \begin{align*}
y^{\prime }&=1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
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1.989 |
|
| \begin{align*}
x^{\prime }&=2 \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
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2.088 |
|
| \begin{align*}
y^{\prime } \ln \left (\frac {y^{\prime }}{4}\right )&=4 x \\
\end{align*} |
[_quadrature] |
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0.446 |
|
| \begin{align*}
x&=\ln \left (y^{\prime }\right )+\sin \left (y^{\prime }\right ) \\
\end{align*} |
[_quadrature] |
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1.989 |
|
| \begin{align*}
x&=y^{\prime }+\arcsin \left (y^{\prime }\right ) \\
\end{align*} |
[_quadrature] |
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0.730 |
|
| \begin{align*}
{y^{\prime }}^{2}+{\mathrm e}^{y^{\prime }}&=x \\
\end{align*} |
[_quadrature] |
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0.260 |
|
| \begin{align*}
y^{\prime }&=x +1 \\
\end{align*} |
[_quadrature] |
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0.344 |
|
| \begin{align*}
y^{\prime }&=1-x \\
\end{align*} |
[_quadrature] |
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0.342 |
|
| \begin{align*}
\cos \left (y^{\prime }\right )&=0 \\
\end{align*} |
[_quadrature] |
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0.644 |
|
| \begin{align*}
{\mathrm e}^{y^{\prime }}&=1 \\
\end{align*} |
[_quadrature] |
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0.404 |
|
| \begin{align*}
\sin \left (y^{\prime }\right )&=x \\
\end{align*} |
[_quadrature] |
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0.241 |
|
| \begin{align*}
\ln \left (y^{\prime }\right )&=x \\
\end{align*} |
[_quadrature] |
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0.312 |
|
| \begin{align*}
\tan \left (y^{\prime }\right )&=0 \\
\end{align*} |
[_quadrature] |
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0.438 |
|
| \begin{align*}
{\mathrm e}^{y^{\prime }}&=x \\
\end{align*} |
[_quadrature] |
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0.217 |
|
| \begin{align*}
\tan \left (y^{\prime }\right )&=x \\
\end{align*} |
[_quadrature] |
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0.273 |
|
| \begin{align*}
x&=\ln \left (y^{\prime }\right )+\sin \left (y^{\prime }\right ) \\
\end{align*} |
[_quadrature] |
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2.934 |
|
| \begin{align*}
x&=\sin \left (y^{\prime }\right )+y^{\prime } \\
\end{align*} |
[_quadrature] |
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0.289 |
|
| \begin{align*}
x^{2}+x y^{\prime }&=3 x +y^{\prime } \\
\end{align*} |
[_quadrature] |
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0.561 |
|
| \begin{align*}
x^{\prime }&=t +2 \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
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0.481 |
|
| \begin{align*}
y^{\prime }&=2 x^{2} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_quadrature] |
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0.904 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right ) \\
y \left (\pi \right ) &= 1 \\
\end{align*} |
[_quadrature] |
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0.503 |
|
| \begin{align*}
x&=y^{\prime } \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[_quadrature] |
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1072.464 |
|
| \begin{align*}
y^{\prime } \left (x -\ln \left (y^{\prime }\right )\right )&=1 \\
\end{align*} |
[_quadrature] |
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1.217 |
|
| \begin{align*}
2 y^{\prime }&=x +\ln \left (y^{\prime }\right ) \\
\end{align*} |
[_quadrature] |
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1.974 |
|