| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 6301 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| 6302 |
\begin{align*}
t^{2} y+y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| 6303 |
\begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=4 x+5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| 6304 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right ) \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| 6305 |
\begin{align*}
x^{\prime }&=4 y \\
y^{\prime }&=-4 x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| 6306 |
\begin{align*}
y&=x {y^{\prime }}^{2}+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| 6307 |
\begin{align*}
2 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| 6308 |
\begin{align*}
2 y+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| 6309 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| 6310 |
\begin{align*}
2 x^{\prime }+y^{\prime }+x+y&=t^{2}+4 t \\
x^{\prime }+y^{\prime }+2 x+2 y&=2 t^{2}-2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| 6311 |
\begin{align*}
\left (1-y^{2}\right ) y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.525 |
|
| 6312 |
\begin{align*}
a \,x^{3} y^{\prime \prime \prime }+b \,x^{2} y^{\prime \prime }+c x y^{\prime }+d y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.526 |
|
| 6313 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\
x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 6314 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 6315 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 6316 |
\begin{align*}
\sin \left (t \right ) y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+\frac {y}{t}&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.526 |
|
| 6317 |
\begin{align*}
y \left (6 y^{2}-x -1\right )+2 y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 6318 |
\begin{align*}
{y^{\prime }}^{2}+y^{\prime } x +1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 6319 |
\begin{align*}
x^{2} y y^{\prime \prime }&=a y^{2}+a x y y^{\prime }+2 x^{2} {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.526 |
|
| 6320 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.526 |
|
| 6321 |
\begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=-2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 6322 |
\begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=5 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 6323 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+2 x_{2} \\
x_{2}^{\prime }&=x_{2}-x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 6324 |
\begin{align*}
-2 y+y^{\prime }&=6 \,{\mathrm e}^{5 t} \\
y \left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 6325 |
\begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 6326 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 6327 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.527 |
|
| 6328 |
\begin{align*}
x^{2} y^{\prime \prime }+a \left (-y+y^{\prime } x \right )^{2}-b \,x^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.527 |
|
| 6329 |
\begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 6330 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 6331 |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 6332 |
\begin{align*}
2 x^{\prime }-x-y^{\prime }+y&=4 t \,{\mathrm e}^{-t}-3 \,{\mathrm e}^{-t} \\
x^{\prime }+4 x-2 y^{\prime }-4 y&=2 t \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 6333 |
\begin{align*}
x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 6334 |
\begin{align*}
y^{\prime \prime }&=f \left (x \right ) y^{2}+y^{3}+y \left (-2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+\left (3 f \left (x \right )-y\right ) y^{\prime } \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.528 |
|
| 6335 |
\begin{align*}
x^{\prime }&=-3 x+\sqrt {2}\, y \\
y^{\prime }&=\sqrt {2}\, x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| 6336 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.528 |
|
| 6337 |
\begin{align*}
\left (x -y\right ) y^{\prime \prime }-\left (1+y^{\prime }\right ) \left (1+{y^{\prime }}^{2}\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.528 |
|
| 6338 |
\begin{align*}
x^{\prime }&=3 x+a y \\
y^{\prime }&=-6 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| 6339 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y&=5 \sqrt {x} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.528 |
|
| 6340 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\alpha ^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| 6341 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=8 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| 6342 |
\begin{align*}
x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime }+x \left (d +a y^{4}\right )+y \left (c +b y^{2}\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.529 |
|
| 6343 |
\begin{align*}
\left (2+x \right )^{2} y^{\prime \prime }+\left (2+x \right ) y^{\prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.529 |
|
| 6344 |
\begin{align*}
\left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| 6345 |
\begin{align*}
\left (x +1\right ) y^{\prime \prime }+3 y^{\prime }-2 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| 6346 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}+7 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 6347 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x +\frac {y}{4}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 6348 |
\begin{align*}
\left (3 x +2\right ) y^{\prime \prime }-y^{\prime } x +2 y x&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 6349 |
\begin{align*}
\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.530 |
|
| 6350 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.530 |
|
| 6351 |
\begin{align*}
2 x^{2} y y^{\prime \prime }-x^{2} \left (1+{y^{\prime }}^{2}\right )+y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.530 |
|
| 6352 |
\begin{align*}
x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 6353 |
\begin{align*}
2 x^{\prime }-y^{\prime }&=t \\
3 x^{\prime }+2 y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 6354 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 y^{\prime } x +2 y&=x^{2}+3 x -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 6355 |
\begin{align*}
x^{2} y^{\prime \prime \prime \prime }&=\lambda y^{\prime \prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.530 |
|
| 6356 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=2 x \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.530 |
|
| 6357 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=\cosh \left (2 x \right ) \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.530 |
|
| 6358 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| 6359 |
\begin{align*}
3 {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.531 |
|
| 6360 |
\begin{align*}
\left (1+y^{2}\right ) y^{\prime \prime }&=3 y {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.531 |
|
| 6361 |
\begin{align*}
2 a^{2} y-a^{2} y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=\sinh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| 6362 |
\begin{align*}
y^{2}-3 y x -2 x^{2}+\left (y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| 6363 |
\begin{align*}
x^{\prime }&=-x+\frac {y}{4} \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| 6364 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| 6365 |
\begin{align*}
5 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| 6366 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=24 x^{2}-6 x +14+32 \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| 6367 |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| 6368 |
\begin{align*}
x^{\prime }+2 y&=4 \,{\mathrm e}^{2 t} \\
x+y^{\prime }-y&=2 \,{\mathrm e}^{2 t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 7 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| 6369 |
\begin{align*}
x^{\prime }&=5 x-6 y+1 \\
y^{\prime }&=6 x-7 y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| 6370 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| 6371 |
\begin{align*}
x_{1}^{\prime }&=-\frac {4 x_{1}}{5}+2 x_{2} \\
x_{2}^{\prime }&=-x_{1}+\frac {6 x_{2}}{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| 6372 |
\begin{align*}
\left (4 x^{2}-24 x +37\right ) y^{\prime \prime }+y&=0 \\
y \left (3\right ) &= 4 \\
y^{\prime }\left (3\right ) &= -6 \\
\end{align*} Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| 6373 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=5 x_{1}+2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| 6374 |
\begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| 6375 |
\begin{align*}
\left (-x^{2}+4 x -3\right ) y^{\prime \prime }-2 \left (x -2\right ) y^{\prime }+6 y&=0 \\
y \left (2\right ) &= 1 \\
y^{\prime }\left (2\right ) &= 0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| 6376 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| 6377 |
\begin{align*}
x^{\prime }&=5 x-6 y+1 \\
y^{\prime }&=6 x-7 y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| 6378 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| 6379 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}+x_{2}+3 x_{3} \\
x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=3 x_{1}+x_{2}+5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| 6380 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=\tan \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| 6381 |
\begin{align*}
x_{1}^{\prime }&=-6 x_{2} \\
x_{2}^{\prime }&=x_{1}-5 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| 6382 |
\begin{align*}
\left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| 6383 |
\begin{align*}
4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| 6384 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.533 |
|
| 6385 |
\begin{align*}
2 t^{3} y^{\prime \prime \prime }+t^{2} y^{\prime \prime }+y^{\prime } t -y&=-3 t^{2} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
y^{\prime \prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| 6386 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.534 |
|
| 6387 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.534 |
|
| 6388 |
\begin{align*}
y^{\prime \prime }&=\sin \left (y\right ) \\
y \left (0\right ) &= \frac {\pi }{4} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.534 |
|
| 6389 |
\begin{align*}
y&=y^{\prime } x +\frac {y {y^{\prime }}^{2}}{x^{2}} \\
\end{align*} |
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✓ |
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0.534 |
|
| 6390 |
\begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (3\right ) &= 1 \\
\end{align*} |
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0.534 |
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| 6391 |
\begin{align*}
2 y+y^{\prime }&=6 \\
\end{align*} |
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0.534 |
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| 6392 |
\begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=5 x-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 15 \\
\end{align*} |
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0.534 |
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| 6393 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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0.534 |
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| 6394 |
\begin{align*}
y^{\left (5\right )}&=120 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 6 \\
y^{\prime \prime \prime \prime }\left (0\right ) &= 24 \\
\end{align*} Using Laplace transform method. |
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0.534 |
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| 6395 |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=x^{3}-x +3 \\
\end{align*} Series expansion around \(x=0\). |
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0.534 |
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| 6396 |
\begin{align*}
y^{\prime \prime }+2 x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
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0.535 |
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| 6397 |
\begin{align*}
-x +y&={y^{\prime }}^{2} \left (1-\frac {2 y^{\prime }}{3}\right ) \\
\end{align*} |
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0.535 |
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| 6398 |
\begin{align*}
y^{\prime \prime }+x^{2} y&=x^{2}+x +1 \\
\end{align*} Series expansion around \(x=0\). |
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0.535 |
|
| 6399 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
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0.535 |
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| 6400 |
\begin{align*}
y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=2 \,{\mathrm e}^{-3 t}-t \,{\mathrm e}^{-t} \\
\end{align*} |
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0.535 |
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