| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 9401 |
\begin{align*}
2 x y^{\prime \prime }+5 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| 9402 |
\begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2} \\
y_{2}^{\prime }&=y_{1}-y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| 9403 |
\begin{align*}
y^{\prime \prime }+9 y&=x \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| 9404 |
\begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=3 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| 9405 |
\begin{align*}
x^{\prime }&=x+y-5 t +2 \\
y^{\prime }&=4 x-2 y-8 t -8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| 9406 |
\begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=7 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.695 |
|
| 9407 |
\begin{align*}
y^{2} {y^{\prime }}^{2}-x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| 9408 |
\begin{align*}
y_{1}^{\prime }&=y_{1}+10 y_{2}-12 y_{3} \\
y_{2}^{\prime }&=2 y_{1}+2 y_{2}+3 y_{3} \\
y_{3}^{\prime }&=2 y_{1}-y_{2}+6 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.696 |
|
| 9409 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}+x_{2} \\
x_{2}^{\prime }&=-2 x_{1}-3 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2}-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.696 |
|
| 9410 |
\begin{align*}
y&=x y^{\prime }+{y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.696 |
|
| 9411 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\mu x} y^{2}+\lambda y-a \,b^{2} {\mathrm e}^{\left (\mu +2 \lambda \right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.696 |
|
| 9412 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=8 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.696 |
|
| 9413 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{1+{\mathrm e}^{-x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.696 |
|
| 9414 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=x_{1}-x_{2}+x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 5 \\
x_{3} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.696 |
|
| 9415 |
\begin{align*}
y_{1}^{\prime }&=5 y_{1}-y_{2}+y_{3} \\
y_{2}^{\prime }&=-y_{1}+9 y_{2}-3 y_{3} \\
y_{3}^{\prime }&=-2 y_{1}+2 y_{2}+4 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| 9416 |
\begin{align*}
y_{1}^{\prime }&=-6 y_{1}-4 y_{2}-4 y_{3} \\
y_{2}^{\prime }&=2 y_{1}-y_{2}+y_{3} \\
y_{3}^{\prime }&=2 y_{1}+3 y_{2}+y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| 9417 |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=-b x_{1}-a x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| 9418 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.697 |
|
| 9419 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{10}+25 y&=\cos \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| 9420 |
\begin{align*}
n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| 9421 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=6 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| 9422 |
\begin{align*}
2 y^{\prime \prime }+x y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.697 |
|
| 9423 |
\begin{align*}
y^{\prime \prime }+8 y^{\prime }+16 y&=\frac {{\mathrm e}^{-4 t}}{t^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| 9424 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| 9425 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y+37 \sin \left (3 x \right )&=0 \\
y \left (\frac {\pi }{2}\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| 9426 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| 9427 |
\begin{align*}
y^{\prime }+y^{\prime \prime \prime }&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| 9428 |
\begin{align*}
\left (2 x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }-6 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| 9429 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=8 \sin \left (2 x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| 9430 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=2 \,{\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| 9431 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-y&=\sinh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| 9432 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{2}} \\
y \left (1\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| 9433 |
\begin{align*}
x^{\prime }&=-3 x-4 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| 9434 |
\begin{align*}
y x -x^{2} y^{\prime }+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| 9435 |
\begin{align*}
y^{\prime \prime }-2 x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| 9436 |
\begin{align*}
y^{\prime \prime }+y&=\frac {1}{\cos \left (x \right )^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| 9437 |
\begin{align*}
x^{\prime }&=-\frac {3 x}{4}-\frac {7 y}{4} \\
y^{\prime }&=\frac {x}{4}+\frac {5 y}{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| 9438 |
\begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=8 x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| 9439 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| 9440 |
\begin{align*}
y^{\prime \prime }-y&=4 x \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| 9441 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| 9442 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \sec \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| 9443 |
\begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u&=3 \cos \left (6 t \right ) \\
u \left (0\right ) &= 2 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| 9444 |
\begin{align*}
x y^{\prime \prime }+\left (2 x +4\right ) y^{\prime }+\left (x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| 9445 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| 9446 |
\begin{align*}
y y^{\prime \prime }-a {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.699 |
|
| 9447 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\
x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| 9448 |
\begin{align*}
\left (x^{3} y^{3}+x^{2} y^{2}+y x +1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-y x +1\right ) x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| 9449 |
\begin{align*}
16 y^{\prime \prime }-8 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| 9450 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| 9451 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=-\frac {{\mathrm e}^{-2 x}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| 9452 |
\begin{align*}
y^{\prime }-2 y-v^{\prime }-v&=6 \,{\mathrm e}^{3 x} \\
2 y^{\prime }-3 y+v^{\prime }-3 v&=6 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.699 |
|
| 9453 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+2 y&=4 \cos \left (3 x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| 9454 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+3 y&=4 \cos \left (3 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| 9455 |
\begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u&=3 \cos \left (\frac {t}{4}\right ) \\
u \left (0\right ) &= 2 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 9456 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (7 x^{2}+3\right ) y^{\prime }+\left (8 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 9457 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=-3 x_{1}+2 x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 9458 |
\begin{align*}
4 y+y^{\prime \prime }&=\sec \left (x \right ) \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 9459 |
\begin{align*}
y^{\prime \prime }+y&=3 \,{\mathrm e}^{x} \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 9460 |
\begin{align*}
4 y+y^{\prime \prime }&=4 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 9461 |
\begin{align*}
y^{\prime \prime }-y&=\frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 9462 |
\begin{align*}
y^{\prime \prime }+y&=2 \cos \left (x \right )-2 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 9463 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
z^{\prime }&=2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 9464 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{t} \ln \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 9465 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\
y \left (-1\right ) &= 2 \\
y^{\prime }\left (-1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 9466 |
\begin{align*}
x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 9467 |
\begin{align*}
x^{2} y^{\prime \prime }&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 9468 |
\begin{align*}
x^{\prime }&=4 x-13 y \\
y^{\prime }&=2 x-6 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 9469 |
\begin{align*}
x^{\prime \prime }-4 x^{\prime }+13 x&=20 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 9470 |
\begin{align*}
x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 9471 |
\begin{align*}
y^{\prime \prime }+9 y&=\sin \left (3 x \right ) \\
y \left (0\right ) &= 1 \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 9472 |
\begin{align*}
y^{\prime \prime }+3 y&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 9473 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=-12 x +8 \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= -11 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 9474 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9475 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{{2}/{3}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9476 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=169 \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9477 |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }+2 x&=85 \sin \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= -20 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9478 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9479 |
\begin{align*}
x^{\prime }&=3 x+4 y \\
y^{\prime }&=3 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9480 |
\begin{align*}
2 y^{\prime \prime }+y^{\prime }-y&=4 \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9481 |
\begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&=t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= -{\frac {5}{16}} \\
y^{\prime }\left (0\right ) &= {\frac {9}{16}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9482 |
\begin{align*}
x^{\prime }&=4 x+2 y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9483 |
\begin{align*}
\left (2-3 y\right )^{2} {y^{\prime }}^{2}&=4-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9484 |
\begin{align*}
x y^{\prime \prime }+{y^{\prime }}^{2} x -y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9485 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=x^{3}+3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9486 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=2 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9487 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=9 x \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9488 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9489 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{i \omega t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9490 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }-2 y x&=x^{2} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.702 |
|
| 9491 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2}-2 x_{3} \\
x_{2}^{\prime }&=x_{1}+6 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+6 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 9492 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-6 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 9493 |
\begin{align*}
\left (2 x +1\right )^{2} y^{\prime \prime \prime }+2 \left (2 x +1\right ) y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.702 |
|
| 9494 |
\begin{align*}
y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 9495 |
\begin{align*}
\left (x^{3} y^{3}+x^{2} y^{2}+y x +1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-y x +1\right ) x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 9496 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+k x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 9497 |
\begin{align*}
x y^{\prime \prime }+\left (x^{3}-1\right ) y^{\prime }+3 x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 9498 |
\begin{align*}
y^{\prime }&=2-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 9499 |
\begin{align*}
x^{\prime }+y^{\prime }&={\mathrm e}^{-t}-y \\
2 x^{\prime }+y^{\prime }&=\sin \left (t \right )-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 9500 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{2}+x_{3} \\
x_{2}^{\prime }&=-2 x_{1}-x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.703 |
|