| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 8501 |
\begin{align*}
y^{\prime \prime }-y \sin \left (x \right )&=\cos \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.625 |
|
| 8502 |
\begin{align*}
y^{\prime }-i y&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| 8503 |
\begin{align*}
y^{\prime \prime }&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| 8504 |
\begin{align*}
x^{\prime }+2 y^{\prime }-2 x+2 y&=3 \,{\mathrm e}^{t} \\
3 x^{\prime }+y^{\prime }+2 x+y&=4 \,{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| 8505 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| 8506 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| 8507 |
\begin{align*}
y^{\prime \prime }+9 y&=f \left (t \right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| 8508 |
\begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| 8509 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| 8510 |
\begin{align*}
\left (x^{2}+4 x +3\right ) y^{\prime \prime }-\left (-x^{2}+4 x +5\right ) y^{\prime }-\left (x +2\right ) y&=0 \\
y \left (-2\right ) &= 2 \\
y^{\prime }\left (-2\right ) &= -1 \\
\end{align*}
Series expansion around \(x=-2\). |
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| 8511 |
\begin{align*}
y^{\prime \prime }+\left (1+\cos \left (x \right )\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| 8512 |
\begin{align*}
-y-2 y^{\prime }+4 y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| 8513 |
\begin{align*}
x +y y^{\prime }+\frac {x y^{\prime }}{x^{2}+y^{2}}-\frac {y}{x^{2}+y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.626 |
|
| 8514 |
\begin{align*}
4 x^{3}-\sin \left (x \right )+y^{3}-\left (y^{2}+1-3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.626 |
|
| 8515 |
\begin{align*}
y^{\prime }&=4 y^{2}-3 y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| 8516 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{1+{\mathrm e}^{-x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.626 |
|
| 8517 |
\begin{align*}
x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| 8518 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-12 y&=0 \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| 8519 |
\begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| 8520 |
\begin{align*}
y_{1}^{\prime }&=-4 y_{1}-y_{3} \\
y_{2}^{\prime }&=-y_{1}-3 y_{2}-y_{3} \\
y_{3}^{\prime }&=y_{1}-2 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| 8521 |
\begin{align*}
{y^{\prime }}^{2}&=x^{2} y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| 8522 |
\begin{align*}
x y^{\prime \prime }&={y^{\prime }}^{3}+y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| 8523 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=6 x +4 \\
y \left (-1\right ) &= 0 \\
y^{\prime }\left (-1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| 8524 |
\begin{align*}
y^{\prime }&=\left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| 8525 |
\begin{align*}
x^{\prime \prime }-3 x^{\prime }-x&=t^{2}+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| 8526 |
\begin{align*}
y^{\prime \prime }+25 y&=\sin \left (5 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| 8527 |
\begin{align*}
y^{\prime \prime }-y&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| 8528 |
\begin{align*}
y^{\prime \prime }+9 y&={\mathrm e}^{2 t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| 8529 |
\begin{align*}
x^{\prime }&=x+9 y \\
y^{\prime }&=-2 x-5 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8530 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+10 y&=24 \,{\mathrm e}^{x} \cos \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8531 |
\begin{align*}
y^{\prime \prime \prime }&=2 \left (y^{\prime \prime }-1\right ) \cot \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8532 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8533 |
\begin{align*}
y^{\prime }+y^{\prime \prime \prime }&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8534 |
\begin{align*}
\left (x^{2}-25\right ) y^{\prime \prime }+2 x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8535 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=3 \,{\mathrm e}^{-x}+2 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8536 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=x^{2} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.628 |
|
| 8537 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=x^{2}+2 x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8538 |
\begin{align*}
x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8539 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8540 |
\begin{align*}
x y^{\prime }+2 y x&=\sqrt {x} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.628 |
|
| 8541 |
\begin{align*}
y^{\prime \prime }+y&=x^{3}+x^{2}+x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8542 |
\begin{align*}
\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.628 |
|
| 8543 |
\begin{align*}
x^{3} y^{\prime \prime }+x y^{\prime }-\left (2 x +3\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.628 |
|
| 8544 |
\(\left [\begin {array}{ccc} 5 & 0 & 0 \\ 4 & -4 & -2 \\ -2 & 12 & 6 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.628 |
|
| 8545 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 1 \\
y \left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8546 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+13 y&=25 \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8547 |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=\sec \left (t \right )^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✗ |
✓ |
✓ |
0.628 |
|
| 8548 |
\begin{align*}
y^{\prime \prime }-4 y&=t \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8549 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
y \left (\frac {\pi }{4}\right ) &= 2 \\
y^{\prime }\left (\frac {\pi }{4}\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8550 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }-4 y&=2 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8551 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8552 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=3 x \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8553 |
\begin{align*}
y^{\prime \prime }-y&=\frac {2}{1+{\mathrm e}^{x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8554 |
\begin{align*}
y^{\prime \prime }+y&=2 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8555 |
\begin{align*}
y^{\prime \prime }+y&=3 x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 8556 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+4 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| 8557 |
\begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| 8558 |
\begin{align*}
y^{\prime \prime }+2 n^{2} y^{\prime }+n^{4} y&=\sin \left (k x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| 8559 |
\begin{align*}
x^{\prime }&=3 x-4 y \\
y^{\prime }&=4 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| 8560 |
\begin{align*}
x^{\prime }&=3 x-4 y \\
y^{\prime }&=4 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| 8561 |
\begin{align*}
y^{\prime \prime }-x y^{\prime }-y x -3 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.629 |
|
| 8562 |
\begin{align*}
f \left (x \right ) y+\left (2+f \left (x \right ) x \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.629 |
|
| 8563 |
\(\left [\begin {array}{ccc} 2 & 0 & 0 \\ -6 & 11 & 2 \\ 6 & -15 & 0 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.629 |
|
| 8564 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{\sqrt {x^{2}-1}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| 8565 |
\begin{align*}
x^{\prime }&=6 x+y \\
y^{\prime }&=4 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| 8566 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{4}/{3}}}-\frac {6}{x^{2}}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.629 |
|
| 8567 |
\begin{align*}
y^{\prime }+z&=t \\
z^{\prime }+4 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
z \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| 8568 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| 8569 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+6 \,{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=x_{1}+x_{2}+2 \,{\mathrm e}^{2 t} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 6 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| 8570 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2}-2 \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 8571 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=5 \,{\mathrm e}^{-2 x} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 8572 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=2 x \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 8573 |
\begin{align*}
x y^{\prime \prime \prime }&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 8574 |
\begin{align*}
\left (x^{2}+a \right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}+b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.630 |
|
| 8575 |
\begin{align*}
y^{\prime \prime }-\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.630 |
|
| 8576 |
\(\left [\begin {array}{ccc} 2 & 0 & 0 \\ 2 & -2 & -1 \\ -2 & 6 & 3 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.630 |
|
| 8577 |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+13 y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 6 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 8578 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=2 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 8579 |
\begin{align*}
\sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 y \sin \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.630 |
|
| 8580 |
\begin{align*}
x^{\prime \prime }+x&=t^{2}-2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 8581 |
\begin{align*}
x^{\prime }+4 x+3 y^{\prime }+4 y&=0 \\
x^{\prime }+2 x+2 y^{\prime }+2 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 8582 |
\begin{align*}
y^{\prime \prime }-y&=4 \cosh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 8583 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 8584 |
\begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=\sin \left (x \right ) \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 8585 |
\begin{align*}
x^{\prime \prime }+8 x^{\prime }+25 x&=200 \cos \left (t \right )+520 \sin \left (t \right ) \\
x \left (0\right ) &= -30 \\
x^{\prime }\left (0\right ) &= -10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 8586 |
\begin{align*}
x_{1}^{\prime }&=-\frac {x_{1}}{4}+x_{2} \\
x_{2}^{\prime }&=-x_{1}-\frac {x_{2}}{4} \\
x_{3}^{\prime }&=-\frac {x_{3}}{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 8587 |
\begin{align*}
4 \left (2-x \right ) {y^{\prime }}^{2}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 8588 |
\begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (3 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 8589 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 8590 |
\begin{align*}
y^{\prime \prime }&=\frac {y^{\prime }}{x \ln \left (x \right )}+\ln \left (x \right )^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.631 |
|
| 8591 |
\begin{align*}
x^{\prime }+2 x-3 y&=t \\
y^{\prime }-3 x+2 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 8592 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 x}}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 8593 |
\begin{align*}
4 y+y^{\prime \prime }&=1-x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 8594 |
\begin{align*}
y^{\prime \prime }+y&=2 \cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 8595 |
\begin{align*}
y^{\prime \prime }+y&=4 x \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 8596 |
\begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u&=3 \cos \left (2 t \right ) \\
u \left (0\right ) &= 2 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| 8597 |
\begin{align*}
y^{\prime \prime }+2 n y^{\prime }+n^{2} y&=5 \cos \left (6 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| 8598 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&=2 x^{2}-4 x -1+2 x^{2} {\mathrm e}^{2 x}+5 x \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| 8599 |
\begin{align*}
f \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| 8600 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+3 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.632 |
|