| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 9401 |
\begin{align*}
x^{\prime }+3 x&={\mathrm e}^{-2 t} \\
x \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9402 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+3 x_{3} \\
x_{2}^{\prime }&=6 x_{1}+4 x_{2}+6 x_{3} \\
x_{3}^{\prime }&=-5 x_{1}-2 x_{2}-4 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= -2 \\
x_{3} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9403 |
\begin{align*}
\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 y y^{\prime } x -x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.701 |
|
| 9404 |
\begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9405 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=3 \delta \left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 9406 |
\begin{align*}
-4 y+3 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=4 \,{\mathrm e}^{x}+3 \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 9407 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\sin \left ({\mathrm e}^{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 9408 |
\begin{align*}
\left (6-9 x \right ) y-\left (4-5 x \right ) x y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.702 |
|
| 9409 |
\begin{align*}
x^{\prime }&=x+z \\
y^{\prime }&=y \\
z^{\prime }&=x+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 9410 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 9411 |
\begin{align*}
y^{\prime \prime \prime }-7 y^{\prime \prime }+20 y^{\prime }-24 y&=-{\mathrm e}^{2 x} \left (\left (13-8 x \right ) \cos \left (2 x \right )-\left (8-4 x \right ) \sin \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| 9412 |
\begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&={\mathrm e}^{\frac {x}{2}} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| 9413 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| 9414 |
\begin{align*}
2 y^{\prime } \left (1+y^{\prime }\right )+\left (x -y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.703 |
|
| 9415 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }-4 y&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| 9416 |
\begin{align*}
y^{\prime }+2 z&=y \\
z^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| 9417 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=3 x \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| 9418 |
\begin{align*}
3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 9419 |
\begin{align*}
2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 9420 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 9421 |
\begin{align*}
6 y x +\left (-x^{3}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 9422 |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (0\right ) &= -4 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.704 |
|
| 9423 |
\begin{align*}
2 y^{\prime \prime }+9 y^{\prime } x -36 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 9424 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 9425 |
\begin{align*}
y^{\prime \prime }-12 y^{\prime }+37 y&={\mathrm e}^{6 t} \sec \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 9426 |
\begin{align*}
y^{\prime \prime }+w^{2} y&=\cos \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 9427 |
\begin{align*}
y&=y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.704 |
|
| 9428 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 9429 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 9430 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=\sin \left ({\mathrm e}^{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 9431 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2}-{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 9432 |
\begin{align*}
x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 9433 |
\begin{align*}
y_{1}^{\prime }&=y_{1}+2 y_{2} \\
y_{2}^{\prime }&=-4 y_{1}+5 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 9434 |
\begin{align*}
x \left (-y x +1\right ) \left (1-y^{2} x^{2}\right ) y^{\prime }+\left (y x +1\right ) \left (1+y^{2} x^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 9435 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \left (\sin \left (x \right )+2 \cos \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 9436 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=3 \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 9437 |
\begin{align*}
x_{1}^{\prime }&=28 x_{1}+50 x_{2}+100 x_{3} \\
x_{2}^{\prime }&=15 x_{1}+33 x_{2}+60 x_{3} \\
x_{3}^{\prime }&=-15 x_{1}-30 x_{2}-57 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 9438 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t}+3 \delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 9439 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}-t^{2} \\
x_{2}^{\prime }&=x_{1}+3 x_{2}+2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 9440 |
\begin{align*}
y^{\prime \prime }-y&=10 \,{\mathrm e}^{2 x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 9441 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-6 x_{2} \\
x_{2}^{\prime }&=3 x_{1}+5 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 9442 |
\begin{align*}
x_{1}^{\prime }&=x_{2}-x_{1} \\
x_{2}^{\prime }&=-2 x_{1}-3 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2}-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 9443 |
\begin{align*}
y^{\prime \prime }-{\mathrm e}^{x} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 9444 |
\begin{align*}
y^{\prime \prime }-2 i y^{\prime }-y&={\mathrm e}^{i x}-2 \,{\mathrm e}^{-i x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 9445 |
\begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.706 |
|
| 9446 |
\begin{align*}
x^{3} y^{\prime }-x^{3}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 9447 |
\begin{align*}
3 y^{2} x^{2}+\left (2 x^{3} y+x^{3} y^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 9448 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=12 \,{\mathrm e}^{-2 x} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 9449 |
\begin{align*}
9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 9450 |
\begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y&=30 \cos \left (x \right )-10 \sin \left (x \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -4 \\
y^{\prime \prime }\left (0\right ) &= 16 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 9451 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {2 \,{\mathrm e}^{-3 x}}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.707 |
|
| 9452 |
\begin{align*}
y^{\prime \prime }+2 x^{2} y^{\prime }+y x&=2 \cos \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.707 |
|
| 9453 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.707 |
|
| 9454 |
\begin{align*}
\left (9 x^{2}+1\right ) y^{\prime \prime }-18 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 9455 |
\begin{align*}
9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.707 |
|
| 9456 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+6\right ) \left (x^{2}-4\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.707 |
|
| 9457 |
\begin{align*}
x^{\prime }&=-2 x-3 y \\
y^{\prime }&=3 x-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 9458 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=\tan \left (2 t \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 9459 |
\begin{align*}
x^{\prime \prime }+x&=\cos \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 9460 |
\begin{align*}
x^{\prime }&=4 x+2 y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 9461 |
\begin{align*}
x^{\prime }&=x-5 y \\
y^{\prime }&=x-3 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 9462 |
\begin{align*}
y^{\prime }+z&=t \\
z^{\prime }+4 y&=0 \\
\end{align*} With initial conditions \begin{align*}
z \left (0\right ) &= -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 9463 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{2 x}}{{\mathrm e}^{2 x}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.707 |
|
| 9464 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=4 \,{\mathrm e}^{x} \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 9465 |
\begin{align*}
y^{\prime \prime }+y&=\frac {1}{x} \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.708 |
|
| 9466 |
\begin{align*}
\left (2 x y^{3}+y\right ) y^{\prime }+2 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 9467 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 9468 |
\begin{align*}
x^{\prime \prime }-s x&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.708 |
|
| 9469 |
\begin{align*}
y^{\prime }+2 y&=5 \delta \left (t -1\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 9470 |
\begin{align*}
y^{\prime \prime \prime }-y&=3 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 9471 |
\begin{align*}
y^{\prime \prime }-9 y&={\mathrm e}^{x}+3 \,{\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 9472 |
\begin{align*}
y^{\prime \prime }+y&=2 \cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 9473 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| 9474 |
\begin{align*}
\sin \left (t \right ) y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+\frac {y}{t}&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.709 |
|
| 9475 |
\begin{align*}
t y^{\prime \prime }+y^{\prime }-4 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| 9476 |
\begin{align*}
y^{\prime \prime }-y&=3 x +5 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| 9477 |
\begin{align*}
x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| 9478 |
\begin{align*}
-2 y x -2 \left (-x^{2}+1\right ) y^{\prime }+x \left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.709 |
|
| 9479 |
\begin{align*}
x^{\prime }&=3 x-y-z \\
y^{\prime }&=x+y-z \\
z^{\prime }&=x-y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| 9480 |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (8\right ) &= -4 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.710 |
|
| 9481 |
\begin{align*}
y^{\prime }+\frac {26 y}{5}&=\frac {97 \sin \left (2 t \right )}{5} \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 9482 |
\begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 9483 |
\begin{align*}
3 y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+\sin \left (y\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.710 |
|
| 9484 |
\begin{align*}
y^{\prime \prime }&=2 y y^{\prime } \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.710 |
|
| 9485 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime } x +4 x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.710 |
|
| 9486 |
\begin{align*}
x^{\prime }&=3 x+5 y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 9487 |
\begin{align*}
y^{\prime \prime }-y&=\sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 9488 |
\begin{align*}
{y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 9489 |
\begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{2} \\
y \left (2\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 9490 |
\begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=2 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 9491 |
\begin{align*}
y_{1}^{\prime }&=y_{1}-2 y_{2} \\
y_{2}^{\prime }&=y_{1}+3 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 9492 |
\begin{align*}
x^{\prime }&=\pi ^{2} x+\frac {187 y}{5} \\
y^{\prime }&=\sqrt {555}\, x+\frac {400617 y}{5000} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 9493 |
\begin{align*}
\sin \left (y \right )^{2}&=x^{\prime } \\
x \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 9494 |
\begin{align*}
x^{\prime }&=4 x-5 y \\
y^{\prime }&=x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 9495 |
\begin{align*}
y_{1}^{\prime }&=-4 y_{1}-y_{2} \\
y_{2}^{\prime }&=y_{1}-2 y_{2} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 9496 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x}+3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 9497 |
\begin{align*}
t y^{\prime \prime }-\left (1+t \right ) y^{\prime }+y&={\mathrm e}^{2 t} t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.712 |
|
| 9498 |
\begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.712 |
|
| 9499 |
\begin{align*}
y_{1}^{\prime }&=-2 y_{2} \\
y_{2}^{\prime }&=y_{1}+2 y_{2} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -1 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.712 |
|
| 9500 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.712 |
|