| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 24401 |
\begin{align*}
4 y+y^{\prime \prime }&=x^{2}+\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
48.868 |
|
| 24402 |
\begin{align*}
y^{\prime \prime }-16 y&=16 t \,{\mathrm e}^{-4 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
48.911 |
|
| 24403 |
\begin{align*}
y^{\prime } x&=y \left (\ln \left (y\right )-\ln \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
48.946 |
|
| 24404 |
\begin{align*}
y+x^{3} \left (3 x^{2}+a \right ) y^{\prime }+x^{6} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
48.953 |
|
| 24405 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda ^{2}+3 a \lambda +a \left (\lambda -a \right ) \cot \left (\lambda x \right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
49.026 |
|
| 24406 |
\begin{align*}
y^{\prime }&=\lambda \arctan \left (x \right )^{n} y^{2}-b \lambda \,x^{m} \arctan \left (x \right )^{n} y+b m \,x^{m -1} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
49.038 |
|
| 24407 |
\begin{align*}
y^{\prime \prime }+y&=2 \,{\mathrm e}^{x}+x^{3}-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.056 |
|
| 24408 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (x^{2}+1\right ) y^{\prime }}{x^{3}}-\frac {y}{x^{4}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
49.106 |
|
| 24409 |
\begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.110 |
|
| 24410 |
\begin{align*}
y^{\prime \prime }+2 n y^{\prime }+n^{2} y&=A \cos \left (p x \right ) \\
y \left (0\right ) &= 9 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.183 |
|
| 24411 |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }+4 x&={\mathrm e}^{t} \cos \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.198 |
|
| 24412 |
\begin{align*}
y y^{\prime }&=\left (2 \ln \left (x \right )^{2}+2 \ln \left (x \right )+a \right ) y+x \left (-\ln \left (x \right )^{4}-a \ln \left (x \right )^{2}+b \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
49.222 |
|
| 24413 |
\begin{align*}
\left (6 x -5 y+4\right ) y^{\prime }&=1+2 x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.236 |
|
| 24414 |
\begin{align*}
3 \sin \left (y\right )-5 x +2 x^{2} \cot \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.255 |
|
| 24415 |
\begin{align*}
z^{\prime }+4 z&={\mathrm e}^{8 i t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.280 |
|
| 24416 |
\begin{align*}
y^{\prime \prime }&=-\frac {x y^{\prime }}{f \left (x \right )}+\frac {y}{f \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.359 |
|
| 24417 |
\begin{align*}
x^{4} y \left (3 y+2 y^{\prime } x \right )+x^{2} \left (4 y+3 y^{\prime } x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.369 |
|
| 24418 |
\begin{align*}
z^{\prime }+4 i z&={\mathrm e}^{8 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.383 |
|
| 24419 |
\begin{align*}
y^{\prime }&=-\frac {x}{2}-\frac {a}{2}+\sqrt {x^{2}+2 a x +a^{2}+4 y}+x^{2} \sqrt {x^{2}+2 a x +a^{2}+4 y}+x^{3} \sqrt {x^{2}+2 a x +a^{2}+4 y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
49.426 |
|
| 24420 |
\begin{align*}
2 y+3 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.435 |
|
| 24421 |
\begin{align*}
x^{\prime }&=7 x+5 y-9 z-8 \,{\mathrm e}^{-2 t} \\
y^{\prime }&=4 x+y+z+2 \,{\mathrm e}^{5 t} \\
z^{\prime }&=-2 y+3 z+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.460 |
|
| 24422 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{2}+y^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
49.518 |
|
| 24423 |
\begin{align*}
y^{\prime }&=y^{2}-\frac {\lambda ^{2}}{2}-\frac {3 \lambda ^{2} \tan \left (\lambda x \right )^{2}}{4}+a \cos \left (\lambda x \right )^{2} \sin \left (\lambda x \right )^{n} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
49.560 |
|
| 24424 |
\begin{align*}
y^{\prime \prime }+25 y&=\cos \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.654 |
|
| 24425 |
\begin{align*}
y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y&=f \left (x \right ) \\
y \left (x_{0} \right ) &= y_{0} \\
y^{\prime }\left (x_{0} \right ) &= y_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.659 |
|
| 24426 |
\begin{align*}
-6 y-2 \left (1-2 x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.671 |
|
| 24427 |
\begin{align*}
2 y^{\prime }&=\left (\lambda +a -\cos \left (\lambda x \right ) a \right ) y^{2}+\lambda -a -\cos \left (\lambda x \right ) a \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.682 |
|
| 24428 |
\begin{align*}
16 y+8 y^{\prime }+y^{\prime \prime }&=8 \,{\mathrm e}^{-2 x} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.718 |
|
| 24429 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=-12 x +8 \\
y \left (1\right ) &= -2 \\
y^{\prime }\left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.718 |
|
| 24430 |
\begin{align*}
y^{\prime \prime }&=\frac {\left (2 x^{2}-1\right ) y^{\prime }}{x^{3}}-\frac {y}{x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.726 |
|
| 24431 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (x -1\right )}-\frac {\left (-v \left (v +1\right ) \left (x -1\right )^{2}-4 n^{2} x \right ) y}{4 x^{2} \left (x -1\right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
49.761 |
|
| 24432 |
\begin{align*}
2 y^{\prime } x -y&=y^{\prime } \ln \left (y y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.765 |
|
| 24433 |
\begin{align*}
y^{\prime \prime }-4 y&=t \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.801 |
|
| 24434 |
\begin{align*}
y+\left (1-x \right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.943 |
|
| 24435 |
\begin{align*}
y^{2}-x \left (2 x +3 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.956 |
|
| 24436 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=x \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.981 |
|
| 24437 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=x \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.004 |
|
| 24438 |
\begin{align*}
p \left (1+2 k +p \right ) y-2 \left (1+k \right ) x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
50.031 |
|
| 24439 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.074 |
|
| 24440 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.189 |
|
| 24441 |
\begin{align*}
y^{\prime }&=\frac {y+\sqrt {x^{2}-y^{2}}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.206 |
|
| 24442 |
\begin{align*}
y^{\prime \prime }-x^{3} y-x^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.333 |
|
| 24443 |
\begin{align*}
2 y+\left (1-x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
50.379 |
|
| 24444 |
\begin{align*}
y^{\prime \prime }+2 y&=-{\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.402 |
|
| 24445 |
\begin{align*}
y^{\prime }&=\frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.497 |
|
| 24446 |
\begin{align*}
x +2 y-1-\left (-5+2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.562 |
|
| 24447 |
\begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.815 |
|
| 24448 |
\begin{align*}
y y^{\prime }-y&=-\frac {6}{25} x -A \,x^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
50.898 |
|
| 24449 |
\begin{align*}
y^{\prime }&=\frac {t}{y^{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.898 |
|
| 24450 |
\begin{align*}
y^{\prime \prime }&=\frac {\left (6 x -1\right ) y^{\prime }}{3 x \left (x -2\right )}+\frac {y}{3 x^{2} \left (x -2\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
51.011 |
|
| 24451 |
\begin{align*}
\left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.023 |
|
| 24452 |
\begin{align*}
x^{\prime \prime }+9 x&=\sin \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.046 |
|
| 24453 |
\begin{align*}
4 y+y^{\prime \prime }&=8 \cos \left (2 x \right )-4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.076 |
|
| 24454 |
\begin{align*}
y^{\prime } x&=\left (x -y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
51.122 |
|
| 24455 |
\begin{align*}
y y^{\prime }-y&=\frac {6}{25} x -A \,x^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
51.166 |
|
| 24456 |
\begin{align*}
y^{\prime \prime }-y&=\sin \left (2 x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.178 |
|
| 24457 |
\begin{align*}
y \sqrt {x^{2}+y^{2}}+y x&=x^{2} y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.198 |
|
| 24458 |
\begin{align*}
\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
51.326 |
|
| 24459 |
\begin{align*}
x^{\prime \prime }-x^{\prime }+x-x^{2}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
51.343 |
|
| 24460 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}-x_{3}+{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=2 x_{1}+3 x_{2}-4 x_{3}+2 \,{\mathrm e}^{2 t} \\
x_{3}^{\prime }&=4 x_{1}+x_{2}-4 x_{3}+{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.382 |
|
| 24461 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }-v \left (v +1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
51.385 |
|
| 24462 |
\begin{align*}
\frac {\left (x^{2}-x \right ) y^{\prime \prime }}{x}+\frac {\left (1+3 x \right ) y^{\prime }}{x}+\frac {y}{x}&=3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
51.418 |
|
| 24463 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.426 |
|
| 24464 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.467 |
|
| 24465 |
\begin{align*}
3 x -y-5+\left (x -y+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.475 |
|
| 24466 |
\begin{align*}
y y^{\prime \prime }&=2 {y^{\prime }}^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= \sqrt {3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
51.638 |
|
| 24467 |
\begin{align*}
2 x \left (x -1\right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }+\left (a x +b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
51.674 |
|
| 24468 |
\begin{align*}
{y^{\prime }}^{2} y^{2} \cos \left (a \right )^{2}-2 y^{\prime } x y \sin \left (a \right )^{2}+y^{2}-x^{2} \sin \left (a \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.691 |
|
| 24469 |
\begin{align*}
y^{\prime } x&=a \sin \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \sin \left (\lambda x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
51.717 |
|
| 24470 |
\begin{align*}
y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}-1}+\frac {v \left (v +1\right ) y}{x^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
51.746 |
|
| 24471 |
\begin{align*}
\left (y^{\prime } x +y\right )^{2}&=y^{2} y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.905 |
|
| 24472 |
\begin{align*}
\left (2 t +1\right ) x^{\prime \prime }+t^{3} x^{\prime }+x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
51.918 |
|
| 24473 |
\begin{align*}
y^{\prime \prime }+9 y&=\sin \left (3 t \right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
51.922 |
|
| 24474 |
\begin{align*}
\left (a -b \right ) y^{2} {y^{\prime }}^{2}-2 b x y y^{\prime }-a b -b \,x^{2}+a y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
51.924 |
|
| 24475 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=4 \cos \left (\ln \left (x +1\right )\right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
51.960 |
|
| 24476 |
\begin{align*}
4 y+y^{\prime \prime }&=\sin \left (3 x \right )+{\mathrm e}^{x}+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.001 |
|
| 24477 |
\begin{align*}
{\mathrm e}^{x} \cos \left (y\right )-x^{2}+\left ({\mathrm e}^{y} \sin \left (x \right )+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
52.081 |
|
| 24478 |
\begin{align*}
16 y+8 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{x}-{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.093 |
|
| 24479 |
\begin{align*}
\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.114 |
|
| 24480 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=24 \,{\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.200 |
|
| 24481 |
\begin{align*}
x^{2}+y^{2}+1+x \left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.263 |
|
| 24482 |
\begin{align*}
x \left (-x^{2}+1\right ) {y^{\prime }}^{2}-2 \left (-x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
52.367 |
|
| 24483 |
\begin{align*}
y \left (\operatorname {a2} +\operatorname {b2} \,x^{k}+\operatorname {c2} \,x^{2 k}+\left (-1+\operatorname {a1} +\operatorname {b1} \,x^{k}\right ) f \left (x \right )+f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+x \left (\operatorname {a1} +\operatorname {b1} \,x^{k}+2 f \left (x \right )\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
52.428 |
|
| 24484 |
\begin{align*}
y^{\prime } x +\cos \left (x^{2}\right )&=827 y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.480 |
|
| 24485 |
\begin{align*}
y^{\prime \prime }+8 y^{\prime }+16 y&=4 \\
y \left (0\right ) &= {\frac {5}{4}} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.517 |
|
| 24486 |
\begin{align*}
x -y \arctan \left (\frac {y}{x}\right )+x \arctan \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.522 |
|
| 24487 |
\begin{align*}
\left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.544 |
|
| 24488 |
\begin{align*}
\left (-2+t \right )^{2} y^{\prime \prime }+5 \left (-2+t \right ) y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.568 |
|
| 24489 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=6 \sin \left (2 x \right )+7 \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.582 |
|
| 24490 |
\begin{align*}
{y^{\prime \prime }}^{2}&=a +b {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.602 |
|
| 24491 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+\left (-x^{2}+2 x +1\right ) y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.607 |
|
| 24492 |
\begin{align*}
x^{2} y^{\prime }+\sin \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {11 \pi }{4} \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
52.648 |
|
| 24493 |
\begin{align*}
y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} \sin \left (x \right )^{m} y-a \sin \left (x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
52.670 |
|
| 24494 |
\begin{align*}
\left (r^{2}+r \right ) R^{\prime \prime }+r R^{\prime }-n \left (n +1\right ) R&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
52.697 |
|
| 24495 |
\begin{align*}
y^{\prime }&=\frac {1+y}{x -y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.755 |
|
| 24496 |
\begin{align*}
y^{\prime }&=\sqrt {a +b \cos \left (y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.784 |
|
| 24497 |
\begin{align*}
2 y^{\prime } t -y&=2 t y^{3} \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.787 |
|
| 24498 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{2}+\sqrt {x^{3}-6 y}+x^{2} \sqrt {x^{3}-6 y}+x^{3} \sqrt {x^{3}-6 y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
52.799 |
|
| 24499 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=5 \,{\mathrm e}^{-2 x} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
52.815 |
|
| 24500 |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
52.824 |
|