| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 11501 |
\begin{align*}
y^{\prime \prime }+9 y&=\sec \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 11502 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +7 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 11503 |
\begin{align*}
x^{\prime }+y&=t^{2} \\
-x+y^{\prime }&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 11504 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 11505 |
\begin{align*}
y^{\prime }&=2 y-5 z \\
z^{\prime }&=4 y-2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 11506 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| 11507 |
\begin{align*}
{y^{\prime }}^{3}+x y^{\prime } y&=2 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.629 |
|
| 11508 |
\begin{align*}
-\left (i x^{2}+p^{2}\right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| 11509 |
\begin{align*}
x^{\prime }&=-x+4 y+2 z \\
y^{\prime }&=4 x-y-2 z \\
z^{\prime }&=6 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| 11510 |
\begin{align*}
y^{\prime \prime } x +\sin \left (x \right ) y^{\prime }+y \cos \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.629 |
|
| 11511 |
\begin{align*}
9 y+6 y^{\prime }+y^{\prime \prime }&=18 \,{\mathrm e}^{-3 x}+8 \sin \left (x \right )+6 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| 11512 |
\begin{align*}
2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (1-t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| 11513 |
\begin{align*}
36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 11514 |
\begin{align*}
f \left (\frac {y^{\prime \prime }}{y^{\prime }}\right ) y^{\prime }&={y^{\prime }}^{2}-y y^{\prime \prime } \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.630 |
|
| 11515 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 11516 |
\begin{align*}
x^{6} {y^{\prime }}^{2}-2 y^{\prime } x -4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 11517 |
\begin{align*}
t^{2} x^{\prime \prime }-2 x&=t^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 11518 | \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right ) \\
y \left (\infty \right ) &= 0 \\
\end{align*} | ✓ | ✓ | ✗ | ✗ | 0.630 |
|
| 11519 |
\begin{align*}
x^{\prime }&=2 x-4 y+1 \\
y^{\prime }&=-x+5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 11520 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 11521 |
\begin{align*}
y^{\prime \prime }+\left (x -1\right )^{2} y^{\prime }-4 \left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 11522 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (1-2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 11523 |
\begin{align*}
y_{1}^{\prime }&=2 y_{2}+y_{3} \\
y_{2}^{\prime }&=-4 y_{1}+6 y_{2}+y_{3} \\
y_{3}^{\prime }&=4 y_{2}+2 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 11524 |
\begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.631 |
|
| 11525 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{2} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.631 |
|
| 11526 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.631 |
|
| 11527 |
\begin{align*}
2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 11528 |
\begin{align*}
y^{\prime \prime }-9 y&=54 t \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 11529 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=6 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 11530 |
\begin{align*}
x^{\prime }+4 x&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 11531 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=x \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 11532 |
\begin{align*}
y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 11533 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| 11534 |
\begin{align*}
y^{\prime \prime }&=2 y^{\prime } y \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.632 |
|
| 11535 |
\begin{align*}
4 x^{2} y^{\prime \prime }+y&=x^{3} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| 11536 |
\begin{align*}
\cos \left (y^{\prime }\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| 11537 | \begin{align*}
x {y^{\prime }}^{2}+a x&=2 y^{\prime } y \\
\end{align*} | ✓ | ✓ | ✗ | ✓ | 0.632 |
|
| 11538 |
\begin{align*}
y^{\prime \prime }&=y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| 11539 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| 11540 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| 11541 |
\begin{align*}
y+y^{\prime }&=\operatorname {Heaviside}\left (t -10\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| 11542 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}-6 x_{3} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}-2 x_{3} \\
x_{3}^{\prime }&=4 x_{1}-2 x_{2}-4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.633 |
|
| 11543 |
\begin{align*}
t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.633 |
|
| 11544 |
\begin{align*}
-y+y^{\prime } x +x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.633 |
|
| 11545 |
\begin{align*}
2 y y^{\prime \prime }&=a +{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.633 |
|
| 11546 |
\begin{align*}
a {y^{\prime }}^{3}+b {y^{\prime }}^{2}+c y^{\prime }-y-d&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.633 |
|
| 11547 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{4}+y&=\delta \left (-1+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.633 |
|
| 11548 |
\begin{align*}
y^{\prime }+3 y+z&=0 \\
z^{\prime }+3 y+5 z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.633 |
|
| 11549 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.633 |
|
| 11550 |
\begin{align*}
y^{\prime }&=y^{2}-y^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.633 |
|
| 11551 |
\begin{align*}
y^{\prime \prime } x&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| 11552 |
\begin{align*}
\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.634 |
|
| 11553 |
\begin{align*}
9 x^{2} y^{\prime \prime }+9 y^{\prime } x -\left (1+3 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| 11554 |
\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*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| 11555 |
\begin{align*}
x^{2} \left (9+4 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| 11556 | \begin{align*}
y_{1}^{\prime }&=3 y_{1}+2 y_{2}-2 y_{3} \\
y_{2}^{\prime }&=-2 y_{1}+7 y_{2}-2 y_{3} \\
y_{3}^{\prime }&=-10 y_{1}+10 y_{2}-5 y_{3} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.634 |
|
| 11557 |
\begin{align*}
y_{1}^{\prime }&=3 y_{1}+y_{2}-y_{3} \\
y_{2}^{\prime }&=3 y_{1}+5 y_{2}+y_{3} \\
y_{3}^{\prime }&=-6 y_{1}+2 y_{2}+4 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| 11558 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=2 \left (t -3\right ) \operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| 11559 |
\begin{align*}
y_{1}^{\prime }-2 y_{1}+3 y_{2}-3 y_{3}&=0 \\
-4 y_{1}+y_{2}^{\prime }+5 y_{2}-3 y_{3}&=0 \\
-4 y_{1}+4 y_{2}+y_{3}^{\prime }-2 y_{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| 11560 |
\begin{align*}
y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| 11561 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x \sin \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.634 |
|
| 11562 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=\cos \left (x \right ) x^{3} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.634 |
|
| 11563 |
\begin{align*}
y^{\prime \prime }-9 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| 11564 |
\begin{align*}
\sqrt {x}\, y^{\prime \prime }+y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| 11565 |
\begin{align*}
x^{\prime }&=8 x+2 y+7 \,{\mathrm e}^{2 t} \\
y^{\prime }&=4 x+y-7 \,{\mathrm e}^{2 t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| 11566 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{4 x^{2}}\right ) y&=\sqrt {x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.634 |
|
| 11567 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| 11568 |
\begin{align*}
\left (-1+t \right ) y^{\prime \prime }-t y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.634 |
|
| 11569 |
\begin{align*}
2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| 11570 |
\begin{align*}
y_{1}^{\prime }&=-2 y_{1}-12 y_{2}+10 y_{3} \\
y_{2}^{\prime }&=2 y_{1}-24 y_{2}+11 y_{3} \\
y_{3}^{\prime }&=2 y_{1}-24 y_{2}+8 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| 11571 |
\begin{align*}
-2 y+y^{\prime \prime }&=\sin \left (2 x \right ) {\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| 11572 |
\begin{align*}
3 y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.635 |
|
| 11573 |
\begin{align*}
y y^{\prime \prime }-y^{2} y^{\prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.635 |
|
| 11574 |
\begin{align*}
x^{2} y^{\prime \prime }&=6 y-4 y^{2} x^{2}+x^{4} {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.635 |
|
| 11575 | \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✗ | 0.635 |
|
| 11576 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| 11577 |
\begin{align*}
x^{8} {y^{\prime }}^{2}+3 y^{\prime } x +9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| 11578 |
\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*} |
✓ |
✓ |
✓ |
✗ |
0.635 |
|
| 11579 |
\begin{align*}
x^{3} y^{\prime \prime }-\left (-y+y^{\prime } x \right )^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.635 |
|
| 11580 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| 11581 |
\begin{align*}
y^{\prime \prime }+4 y&=\tan \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| 11582 |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=\tan \left (t \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| 11583 |
\begin{align*}
x^{\prime \prime }+x&=\cos \left (\frac {7 t}{10}\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| 11584 |
\begin{align*}
x^{\prime \prime }+16 x&=t \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| 11585 |
\begin{align*}
y^{\prime \prime }-y&=\frac {{\mathrm e}^{x}-{\mathrm e}^{-x}}{{\mathrm e}^{x}+{\mathrm e}^{-x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| 11586 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{16}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| 11587 |
\begin{align*}
x_{1}^{\prime }&=-15 x_{1}-7 x_{2}+4 x_{3} \\
x_{2}^{\prime }&=34 x_{1}+16 x_{2}-11 x_{3} \\
x_{3}^{\prime }&=17 x_{1}+7 x_{2}+5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| 11588 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| 11589 |
\begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| 11590 |
\begin{align*}
2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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0.636 |
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| 11591 |
\begin{align*}
y^{\prime \prime }-y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
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0.636 |
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| 11592 |
\begin{align*}
u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u&=0 \\
\end{align*} |
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0.636 |
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| 11593 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x -x^{2}-x&=0 \\
\end{align*} |
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0.636 |
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| 11594 | \begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\mu x} y^{2}+\lambda y-a \,b^{2} {\mathrm e}^{\left (2 \lambda +\mu \right ) x} \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 0.636 |
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| 11595 |
\begin{align*}
y^{\prime \prime }-10 y^{\prime }+25 y&={\mathrm e}^{5 t} \ln \left (2 t \right ) \\
\end{align*} |
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0.636 |
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| 11596 |
\begin{align*}
y^{\prime \prime }-t y&=\frac {1}{\pi } \\
\end{align*} |
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0.636 |
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| 11597 |
\begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=2 x-2 y \\
\end{align*} |
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0.636 |
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| 11598 |
\begin{align*}
y y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
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0.636 |
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| 11599 |
\begin{align*}
y^{\prime \prime }+y&=x^{2} \cos \left (5 x \right ) \\
\end{align*} |
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0.636 |
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| 11600 |
\begin{align*}
y_{1}^{\prime }&=2 y_{1}+y_{2}+{\mathrm e}^{t} \\
y_{2}^{\prime }&=y_{1}+2 y_{2}-{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
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0.636 |
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