| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 11501 |
\begin{align*}
y&={y^{\prime }}^{2}+2 {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
0.913 |
|
| 11502 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=t^{{5}/{2}} {\mathrm e}^{-2 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| 11503 |
\begin{align*}
y y^{\prime \prime }&=-x^{2} y^{2}+\ln \left (y\right ) y^{2}+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.914 |
|
| 11504 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2}+2 \,{\mathrm e}^{-t} \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+3 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| 11505 |
\(\left [\begin {array}{cccc} 1 & 2 & 2 & 2 \\ 0 & 2 & 2 & 2 \\ 0 & 0 & 3 & 2 \\ 0 & 0 & 0 & 4 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.914 |
|
| 11506 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\frac {1}{{\mathrm e}^{2 x}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.914 |
|
| 11507 |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }+x&={\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| 11508 |
\begin{align*}
y^{\prime }&=x^{2}+{\mathrm e}^{x}-\sin \left (x \right ) \\
y \left (2\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| 11509 |
\begin{align*}
y^{\prime }&=4 y+8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| 11510 |
\begin{align*}
y^{\prime \prime \prime }+10 y^{\prime \prime }+34 y^{\prime }+40 y&=t \,{\mathrm e}^{-4 t}+2 \,{\mathrm e}^{-3 t} \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| 11511 |
\begin{align*}
y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=a \sin \left (n x +\alpha \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| 11512 |
\begin{align*}
y^{\prime \prime }&=\operatorname {a0} +\operatorname {a2} y+\operatorname {a1} x y+\operatorname {a3} y^{3} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.915 |
|
| 11513 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| 11514 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+3 y&=x^{2} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.915 |
|
| 11515 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| 11516 |
\begin{align*}
4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| 11517 |
\begin{align*}
y-x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.915 |
|
| 11518 |
\begin{align*}
y \cos \left (y x \right )-\sin \left (x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.916 |
|
| 11519 |
\begin{align*}
y^{\prime }+y&=\epsilon y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.916 |
|
| 11520 |
\begin{align*}
3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| 11521 |
\begin{align*}
y^{\prime \prime }+\left ({\mathrm e}^{-2 x}-\frac {1}{9}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| 11522 |
\begin{align*}
\left (x^{2}-1\right )^{2} y^{\prime \prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| 11523 |
\begin{align*}
x^{\prime }&=-x+y-z \\
y^{\prime }&=2 x-y+2 z \\
z^{\prime }&=2 x+2 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| 11524 |
\begin{align*}
u^{\prime \prime }-\left (x +1\right ) u^{\prime }+\left (x -1\right ) u&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.917 |
|
| 11525 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (3 x^{2}+2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| 11526 |
\begin{align*}
x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| 11527 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.918 |
|
| 11528 |
\begin{align*}
y_{1}^{\prime }&=2 y_{2} \\
y_{2}^{\prime }&=3 y_{1} \\
y_{3}^{\prime }&=2 y_{3}-y_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| 11529 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+20 y&=x^{3} \sin \left (4 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| 11530 |
\begin{align*}
y^{\prime \prime }+{\mathrm e}^{-2 y}&=0 \\
y \left (3\right ) &= 0 \\
y^{\prime }\left (3\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.918 |
|
| 11531 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| 11532 |
\begin{align*}
x^{\prime }&=-7 x+y-6 z \\
y^{\prime }&=10 x-4 y+12 z \\
z^{\prime }&=2 x-y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.919 |
|
| 11533 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{2}+x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.919 |
|
| 11534 |
\begin{align*}
\left (2 x -1\right ) y^{\prime \prime }-\left (3 x -4\right ) y^{\prime }+\left (x -3\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.919 |
|
| 11535 |
\begin{align*}
a b y \left (-1+y\right ) y^{\prime \prime }-\left (\left (2 a b -a -b \right ) y+\left (1-a \right ) b \right ) {y^{\prime }}^{2}+f y \left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.919 |
|
| 11536 |
\begin{align*}
y^{\prime \prime }+4 y&=\cos \left (2 t \right )+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.919 |
|
| 11537 |
\begin{align*}
y^{\prime }-2 y&=\left \{\begin {array}{cc} 1-x & x <1 \\ 0 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| 11538 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{49}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| 11539 |
\begin{align*}
x^{\prime }&=x+2 y+2 t +1 \\
y^{\prime }&=5 x+y+3 t -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| 11540 |
\begin{align*}
y^{\prime \prime }+{\mathrm e}^{x} \sin \left (y\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.920 |
|
| 11541 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.920 |
|
| 11542 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{x} \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (1\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| 11543 |
\begin{align*}
x_{1}^{\prime }&=x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| 11544 |
\begin{align*}
x^{3} y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.920 |
|
| 11545 |
\begin{align*}
y^{\prime \prime }&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| 11546 |
\begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| 11547 |
\begin{align*}
y^{\prime }&=\sqrt {x} \\
y \left (4\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| 11548 |
\begin{align*}
y_{1}^{\prime }&=4 y_{1}-8 y_{2}-4 y_{3} \\
y_{2}^{\prime }&=-3 y_{1}-y_{2}-4 y_{3} \\
y_{3}^{\prime }&=y_{1}-y_{2}+9 y_{3} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -4 \\
y_{2} \left (0\right ) &= 1 \\
y_{3} \left (0\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| 11549 |
\begin{align*}
y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| 11550 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-y&={\mathrm e}^{x} \sin \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| 11551 |
\begin{align*}
y^{2} y^{\prime \prime }+y^{\prime \prime }+2 y {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.921 |
|
| 11552 |
\begin{align*}
y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| 11553 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}+n^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| 11554 |
\begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| 11555 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y&=x^{2}+\frac {1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| 11556 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| 11557 |
\begin{align*}
y^{\prime }&=x \sin \left (x^{2}\right ) \\
y \left (\frac {\sqrt {2}\, \sqrt {\pi }}{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| 11558 |
\begin{align*}
x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (-3 x +1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| 11559 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (-x^{2}+x \right ) y^{\prime }+\left (x^{3}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| 11560 |
\begin{align*}
4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.922 |
|
| 11561 |
\begin{align*}
2 y y^{\prime \prime }&=4 y^{2} \left (x +2 y\right )+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.922 |
|
| 11562 |
\begin{align*}
-y^{\prime }+x y^{\prime \prime }&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| 11563 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| 11564 |
\begin{align*}
y^{\prime \prime }-2 x y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| 11565 |
\begin{align*}
t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.923 |
|
| 11566 |
\begin{align*}
y&=x y^{\prime }+y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.923 |
|
| 11567 |
\begin{align*}
y^{\prime }&={\mathrm e}^{a x}+a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.923 |
|
| 11568 |
\begin{align*}
2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y x&=x^{2}+2 x \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.923 |
|
| 11569 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=9 x^{2}+4 \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.923 |
|
| 11570 |
\begin{align*}
w^{\prime }&=\left (3-w\right ) \left (w+1\right ) \\
w \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.923 |
|
| 11571 |
\begin{align*}
y^{\prime \prime }&=-{\mathrm e}^{-y} y^{\prime } \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.923 |
|
| 11572 |
\begin{align*}
x_{1}^{\prime }&=35 x_{1}-12 x_{2}+4 x_{3}+30 x_{4} \\
x_{2}^{\prime }&=22 x_{1}-8 x_{2}+3 x_{3}+19 x_{4} \\
x_{3}^{\prime }&=-10 x_{1}+3 x_{2}-9 x_{4} \\
x_{4}^{\prime }&=-27 x_{1}+9 x_{2}-3 x_{3}-23 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| 11573 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-x^{2}-6 x +1\right ) y^{\prime }+\left (x^{2}+6 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| 11574 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+5 x_{2}+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\
x_{2}^{\prime }&=-2 x_{1}-2 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| 11575 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (-2 x^{5}+9 x \right ) y^{\prime }+\left (10 x^{4}+5 x^{2}+25\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.924 |
|
| 11576 |
\begin{align*}
y^{\prime \prime }+9 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| 11577 |
\begin{align*}
4 x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| 11578 |
\begin{align*}
y^{\prime \prime }-y&=\cos \left (x \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (2\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| 11579 |
\begin{align*}
y^{\prime \prime }-4 x y^{\prime }-4 y&={\mathrm e}^{x} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.924 |
|
| 11580 |
\begin{align*}
y^{\prime \prime }+\left (\frac {1}{x}-\frac {1}{3}\right ) y^{\prime }+\left (\frac {1}{x}-\frac {1}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| 11581 |
\begin{align*}
x^{\prime }&=2 x-4 y+1 \\
y^{\prime }&=-x+5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| 11582 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 t}}{t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| 11583 |
\begin{align*}
\frac {1}{x}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| 11584 |
\begin{align*}
4 y+y^{\prime \prime }&=20 \,{\mathrm e}^{x}-20 \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| 11585 |
\begin{align*}
x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| 11586 |
\begin{align*}
x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (5+4 x \right ) y^{\prime }-\left (1-2 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| 11587 |
\begin{align*}
y_{1}^{\prime }&=y_{1}-y_{2}-2 y_{3} \\
y_{2}^{\prime }&=y_{1}-2 y_{2}-3 y_{3} \\
y_{3}^{\prime }&=-4 y_{1}+y_{2}-y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| 11588 |
\begin{align*}
2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| 11589 |
\begin{align*}
x -2 y x +{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.925 |
|
| 11590 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| 11591 |
\begin{align*}
x \left (x^{2}-4\right ) y^{\prime }&=1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| 11592 |
\begin{align*}
x^{2} y^{\prime \prime }&=\left (3 x -2 y^{\prime }\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| 11593 |
\begin{align*}
y^{\prime \prime }+2 x y^{\prime }+5 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| 11594 |
\begin{align*}
y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y-{\mathrm e}^{x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.925 |
|
| 11595 |
\begin{align*}
x^{\prime \prime }-2 x^{\prime }+x&=\frac {{\mathrm e}^{t}}{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| 11596 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=4 \,{\mathrm e}^{x} \cos \left (x \right ) \\
y \left (\pi \right ) &= \pi \,{\mathrm e}^{\pi } \\
y^{\prime }\left (\pi \right ) &= {\mathrm e}^{\pi } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| 11597 |
\begin{align*}
\left (8 {y^{\prime }}^{3}-27\right ) x&=12 y {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.925 |
|
| 11598 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| 11599 |
\begin{align*}
x \left (1-2 x \right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+8 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.925 |
|
| 11600 |
\begin{align*}
x_{1}^{\prime }&=-8 x_{1}-11 x_{2}-2 x_{3} \\
x_{2}^{\prime }&=6 x_{1}+9 x_{2}+2 x_{3} \\
x_{3}^{\prime }&=-6 x_{1}-6 x_{2}+x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 5 \\
x_{2} \left (0\right ) &= -7 \\
x_{3} \left (0\right ) &= 11 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.926 |
|