| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 4401 |
\begin{align*}
y^{\prime \prime }+\frac {y}{2 x^{4}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.343 |
|
| 4402 |
\begin{align*}
y^{\prime \prime }-9 y&=24 \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.343 |
|
| 4403 |
\begin{align*}
x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.343 |
|
| 4404 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+3 x^{2} y&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.343 |
|
| 4405 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.343 |
|
| 4406 |
\begin{align*}
y^{\prime \prime }&=y^{\prime }+y \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.344 |
|
| 4407 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x +2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.344 |
|
| 4408 |
\begin{align*}
y^{\prime \prime }&=f \left (a x +b y, y^{\prime }\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.344 |
|
| 4409 |
\begin{align*}
1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.344 |
|
| 4410 |
\begin{align*}
\left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.344 |
|
| 4411 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.344 |
|
| 4412 |
\begin{align*}
x^{\prime }&=4 x+2 y \\
y^{\prime }&=2 x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.344 |
|
| 4413 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.344 |
|
| 4414 |
\begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.344 |
|
| 4415 |
\begin{align*}
y^{\prime \prime }+8 y^{\prime }+7 y&=165 \,{\mathrm e}^{4 t} \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.344 |
|
| 4416 |
\begin{align*}
\left (2 x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.344 |
|
| 4417 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.344 |
|
| 4418 |
\begin{align*}
y^{\prime \prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.344 |
|
| 4419 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| 4420 |
\begin{align*}
x^{\prime \prime }+4 x&=0 \\
x \left (0\right ) &= 5 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| 4421 |
\begin{align*}
y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y&=0 \\
y \left (-1\right ) &= 0 \\
y^{\prime }\left (-1\right ) &= 1 \\
\end{align*} Series expansion around \(t=-1\). |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| 4422 |
\begin{align*}
x^{\prime }-x-2 y&=0 \\
x-y^{\prime }&=15 \cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= x_{0} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| 4423 |
\begin{align*}
\left (-x^{3}+3 x^{2}-6 x +6\right ) y^{\prime \prime }+x \left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.345 |
|
| 4424 |
\begin{align*}
{\mathrm e}^{x}+{\mathrm e}^{y} \left (1+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| 4425 |
\begin{align*}
4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.345 |
|
| 4426 |
\begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-5 x+4 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| 4427 |
\begin{align*}
x^{\prime }&=\frac {1}{\sqrt {t^{2}+1}} \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| 4428 |
\begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=-3 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| 4429 |
\begin{align*}
x^{2} y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| 4430 |
\begin{align*}
x^{\prime }&=-4 x+y \\
y^{\prime }&=-x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| 4431 |
\begin{align*}
y y^{\prime }&=1-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| 4432 |
\begin{align*}
y^{\prime }&=-x \,{\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| 4433 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}+3 x_{2} \\
x_{2}^{\prime }&=-3 x_{1}+5 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| 4434 |
\begin{align*}
4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.346 |
|
| 4435 |
\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*} |
✓ |
✓ |
✓ |
✗ |
0.346 |
|
| 4436 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{-2 x}&={\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.346 |
|
| 4437 |
\begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=-2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| 4438 |
\begin{align*}
x^{\prime }&=-3 x+4 y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| 4439 |
\begin{align*}
\left (x +1\right ) y^{\prime }&=y p \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| 4440 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{-t} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| 4441 |
\begin{align*}
4 i^{\prime \prime }+i&=t^{2}+2 \cos \left (4 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| 4442 |
\begin{align*}
y^{\prime \prime \prime \prime }+16 y^{\prime \prime }&=64 \cos \left (4 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| 4443 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=9 x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.347 |
|
| 4444 |
\begin{align*}
y^{\prime }&=x \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.347 |
|
| 4445 |
\begin{align*}
\frac {x}{x^{2}+y^{2}}+\frac {y}{x^{2}}+\left (\frac {y}{x^{2}+y^{2}}-\frac {1}{x}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.347 |
|
| 4446 |
\begin{align*}
y+x^{3} y+2 x^{2}+\left (x +4 y^{4} x +8 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.347 |
|
| 4447 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.347 |
|
| 4448 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=\delta \left (t \right ) \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.347 |
|
| 4449 |
\begin{align*}
{y^{\prime }}^{2}-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.347 |
|
| 4450 |
\begin{align*}
\left (1-x \right ) x^{2} y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.347 |
|
| 4451 |
\begin{align*}
\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.347 |
|
| 4452 |
\begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2}+1+2 x y^{2}+a y^{3}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.347 |
|
| 4453 |
\begin{align*}
x^{\prime }&=-3 x-y \\
y^{\prime }&=4 x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.347 |
|
| 4454 |
\begin{align*}
y^{\prime }+y^{2}-2 \sin \left (x \right ) y+\sin \left (x \right )^{2}-\cos \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.347 |
|
| 4455 |
\begin{align*}
6 y^{\prime \prime } x +6 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.347 |
|
| 4456 |
\begin{align*}
y^{\prime \prime }&=2 y {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.347 |
|
| 4457 |
\begin{align*}
y_{1}^{\prime }&=3 y_{1}-4 y_{2} \\
y_{2}^{\prime }&=y_{1}-y_{2} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.347 |
|
| 4458 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 4459 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
y \left (0\right ) &= -3 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 4460 |
\begin{align*}
9 \left (x +3\right ) x^{2} y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (4 x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 4461 |
\begin{align*}
y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=\sin \left (3 x \right )+x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 4462 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=15 \,{\mathrm e}^{3 x} \sqrt {x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 4463 |
\begin{align*}
y^{\prime }+2 \left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 4464 |
\begin{align*}
y^{\prime }&=\frac {1}{1+\sin \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 4465 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 4466 |
\begin{align*}
x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 4467 |
\begin{align*}
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 4468 |
\begin{align*}
y^{2} y^{\prime \prime }&=x \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.348 |
|
| 4469 |
\begin{align*}
y^{\prime }&=3 \sin \left (x \right ) \\
y \left (\pi \right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 4470 |
\begin{align*}
x^{\prime }+6 x+3 y^{\prime }+2 y&=0 \\
x^{\prime }+5 x+2 y^{\prime }+3 y&=0 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 4471 |
\begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 4472 |
\begin{align*}
x_{1}^{\prime }&=9 x_{1}+5 x_{2} \\
x_{2}^{\prime }&=-6 x_{1}-2 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 4473 |
\begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 4474 |
\begin{align*}
y^{\prime }+y^{2}+14 y+50&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 4475 |
\begin{align*}
x y^{\prime \prime \prime }+2 y^{\prime \prime }&=A x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 4476 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }&=30 \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 4477 |
\begin{align*}
x^{\prime }&=-4 x-y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 4478 |
\begin{align*}
y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 4479 |
\begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=2 x+5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 4480 |
\begin{align*}
y^{\prime }&=\left (\cos \left (x \right )+y\right )^{2}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 4481 |
\begin{align*}
x^{\prime }&=-3 x+\frac {5 y}{2} \\
y^{\prime }&=-\frac {5 x}{2}+2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 4482 |
\begin{align*}
x^{\prime }&=2 x+\frac {y}{2} \\
y^{\prime }&=-\frac {x}{2}+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 4483 |
\begin{align*}
x^{\prime }&=4 x-3 y \\
y^{\prime }&=8 x-6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 4484 |
\begin{align*}
x^{\prime }&=5 x-6 y \\
y^{\prime }&=6 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 4485 |
\begin{align*}
y^{\prime }&=2 \,{\mathrm e}^{2 t}-4 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 4486 |
\begin{align*}
y^{\prime }&=\cos \left (2 x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| 4487 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=4 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| 4488 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +8 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| 4489 |
\begin{align*}
5 x^{3} y^{2}+2 y+\left (3 x^{4} y+2 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.350 |
|
| 4490 |
\begin{align*}
x^{\prime }&=2 \sin \left (t \right )^{2} \\
x \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| 4491 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x -4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| 4492 |
\begin{align*}
y^{\prime }+2 y-y^{2}&=-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| 4493 |
\begin{align*}
y^{\prime }&=\frac {\sqrt {x^{2}-16}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| 4494 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| 4495 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| 4496 |
\begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| 4497 |
\begin{align*}
y^{\prime }+6 y&=x^{\prime } \\
3 x-x^{\prime }&=2 y^{\prime } \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| 4498 |
\begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=\left (x^{2}+1\right )^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.350 |
|
| 4499 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| 4500 |
\begin{align*}
y^{\prime }&={\mathrm e}^{2 t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.351 |
|