| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 9301 |
\begin{align*}
5 y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.995 |
|
| 9302 |
\begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }-a^{2} y^{\prime }+2 a^{2} y-\sinh \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.995 |
|
| 9303 |
\begin{align*}
y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.996 |
|
| 9304 |
\begin{align*}
h \left (y\right ) y^{\prime \prime }+a h \left (y\right ) {y^{\prime }}^{2}+j \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.996 |
|
| 9305 |
\begin{align*}
x^{4} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| 9306 |
\begin{align*}
t^{2} x^{\prime \prime }+3 t x^{\prime }&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| 9307 |
\begin{align*}
2 v^{\prime }+2 v+w^{\prime }-w&=3 x \\
v^{\prime }+v+w^{\prime }+w&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| 9308 |
\begin{align*}
x_{1}^{\prime }&=x_{2}+f_{1} \left (t \right ) \\
x_{2}^{\prime }&=-x_{1}+f_{2} \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.998 |
|
| 9309 |
\begin{align*}
2 x^{2} y^{\prime \prime }+2 y^{\prime } x -y x&=\sin \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.998 |
|
| 9310 |
\begin{align*}
y^{\prime \prime }+\cos \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.998 |
|
| 9311 |
\begin{align*}
x^{\prime }&=4 x+3 y-6 \,{\mathrm e}^{3 t} \\
y^{\prime }&=x+6 y+2 \,{\mathrm e}^{3 t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.998 |
|
| 9312 |
\begin{align*}
y^{\prime }&=\frac {x -2 y+5}{-4-2 x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.999 |
|
| 9313 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{3}+\cos \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.999 |
|
| 9314 |
\begin{align*}
2 x^{2} y^{\prime \prime }+2 y^{\prime } x -y x&=\cos \left (x \right ) \sin \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.999 |
|
| 9315 |
\begin{align*}
x^{\prime }-5 x+y^{\prime }+2 z&=24 \,{\mathrm e}^{-t} \\
x^{\prime }-x-y&=0 \\
5 y^{\prime }-11 y+2 z^{\prime }-2 z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.999 |
|
| 9316 |
\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*} |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| 9317 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (2 t \right ) \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| 9318 |
\begin{align*}
x^{\prime }&=y+\textit {f\_1} \left (t \right ) \\
y^{\prime }&=-x+f_{2} \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| 9319 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}+6 x_{3} \\
x_{2}^{\prime }&=-2 x_{1}+x_{2}-2 x_{3} \\
x_{3}^{\prime }&=-x_{1}-2 x_{2}-4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| 9320 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-2 x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}-4 x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{1}+2 x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| 9321 |
\begin{align*}
9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.000 |
|
| 9322 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x -3}+\frac {y}{x -4}&=0 \\
\end{align*} Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| 9323 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| 9324 |
\begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 4 & 0\le t <2 \\ 8 t & 2\le t <\infty \end {array}\right . \\
\end{align*} Using Laplace transform method. |
✓ |
✗ |
✓ |
✓ |
1.000 |
|
| 9325 |
\begin{align*}
3 y^{\prime }&=4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| 9326 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-x_{2}+1 \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.001 |
|
| 9327 |
\begin{align*}
4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.002 |
|
| 9328 |
\begin{align*}
y^{\prime }+2 y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.002 |
|
| 9329 |
\begin{align*}
y^{\prime }&=\frac {y^{2}+\tan \left (x \right ) y+\tan \left (x \right )^{2}}{\sin \left (x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.003 |
|
| 9330 |
\begin{align*}
3 x y^{2}+6 x^{2} y y^{\prime }+x^{3} {y^{\prime }}^{2}+x^{3} y y^{\prime \prime }&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.003 |
|
| 9331 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.003 |
|
| 9332 |
\begin{align*}
\left (1+3 x \right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.003 |
|
| 9333 |
\begin{align*}
y^{\prime }&=y^{3}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 9334 |
\begin{align*}
x^{2}+2 y+4 \left (x +y\right ) y^{\prime }+2 x {y^{\prime }}^{2}+x \left (x +2 y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.004 |
|
| 9335 |
\begin{align*}
y^{\prime \prime }-{\mathrm e}^{2 x} y^{\prime }+\cos \left (x \right ) y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 9336 |
\begin{align*}
2 y^{\prime \prime } x -y^{\prime }+x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 9337 |
\begin{align*}
y^{\prime }&=x -2 y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 9338 |
\begin{align*}
5 y^{\prime \prime }-2 y^{\prime } x +10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.004 |
|
| 9339 |
\begin{align*}
v^{\prime }-2 v+2 w^{\prime }&=2-4 \,{\mathrm e}^{2 x} \\
2 v^{\prime }-3 v+3 w^{\prime }-w&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 9340 |
\begin{align*}
4 x^{2} y^{\prime \prime }+\left (1-2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| 9341 |
\begin{align*}
3 y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.005 |
|
| 9342 |
\begin{align*}
y_{1}^{\prime }&=2 y_{1}-3 y_{2}+4 x -2 \\
y_{2}^{\prime }&=y_{1}-2 y_{2}+3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| 9343 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+9 x_{4} \\
x_{2}^{\prime }&=4 x_{1}+2 x_{2}-10 x_{4} \\
x_{3}^{\prime }&=-x_{3}+8 x_{4} \\
x_{4}^{\prime }&=x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| 9344 |
\begin{align*}
{y^{\prime }}^{4}&=\left (y-a \right )^{3} \left (y-b \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| 9345 |
\begin{align*}
2 \left (1-y\right )^{2} y-2 x \left (1-y\right ) y^{\prime }+2 x^{2} {y^{\prime }}^{2}+x^{2} \left (1-y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.006 |
|
| 9346 |
\begin{align*}
y^{\prime \prime } x -4 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| 9347 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 9348 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.007 |
|
| 9349 |
\begin{align*}
y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+32 y^{\prime \prime }+64 y^{\prime }+39 y&={\mathrm e}^{-2 x} \left (\left (4-15 x \right ) \cos \left (3 x \right )-\left (4+15 x \right ) \sin \left (3 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 9350 |
\begin{align*}
x^{\prime }&=2 x-3 y \\
y^{\prime }&=5 x+6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 9351 |
\begin{align*}
y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.008 |
|
| 9352 |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }+12 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| 9353 |
\begin{align*}
{y^{\prime }}^{2}-y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.009 |
|
| 9354 |
\begin{align*}
x^{\prime }&=4 x \left (7-x\right ) \\
x \left (0\right ) &= 11 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 9355 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 9356 |
\begin{align*}
b y+a {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.011 |
|
| 9357 |
\begin{align*}
x \left (x +y\right ) y^{\prime \prime }+x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.011 |
|
| 9358 |
\begin{align*}
y^{\prime }+y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 9359 |
\begin{align*}
y^{\prime }&=x +y \\
y \left (-2\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.012 |
|
| 9360 |
\begin{align*}
\left (x -3\right )^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
1.012 |
|
| 9361 |
\begin{align*}
y^{\prime }-6 y&={\mathrm e}^{6 t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.012 |
|
| 9362 |
\begin{align*}
y y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.013 |
|
| 9363 |
\begin{align*}
t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.013 |
|
| 9364 |
\begin{align*}
y^{\prime } x +y&=x^{4} {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 9365 |
\begin{align*}
y^{\prime } x&=y^{2} x^{2}-y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 9366 |
\begin{align*}
x^{\prime }&=10 x-x^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.014 |
|
| 9367 |
\begin{align*}
2 y^{\prime \prime } x +y^{\prime }-x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.014 |
|
| 9368 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.014 |
|
| 9369 |
\begin{align*}
\left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
1.014 |
|
| 9370 |
\begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.014 |
|
| 9371 |
\begin{align*}
y^{\prime } \left (x -\ln \left (y^{\prime }\right )\right )&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.015 |
|
| 9372 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.015 |
|
| 9373 |
\begin{align*}
\left (a^{2}-x^{2}\right ) \left (a^{2}-y^{2}\right ) y^{\prime \prime }+\left (a^{2}-x^{2}\right ) y {y^{\prime }}^{2}-x \left (a^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.015 |
|
| 9374 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+2 \sin \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.015 |
|
| 9375 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2}-x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}+3 x_{3} \\
x_{3}^{\prime }&=3 x_{1}-4 x_{2}-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.015 |
|
| 9376 |
\begin{align*}
2 x^{\prime }+3 x-y&={\mathrm e}^{t} \\
5 x-3 y^{\prime }&=y+2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| 9377 |
\begin{align*}
y^{\prime }&=\frac {\left (4 \,{\mathrm e}^{-x^{2}}-4 x^{2} {\mathrm e}^{-x^{2}}+4 y^{2}-4 x^{2} {\mathrm e}^{-x^{2}} y+{\mathrm e}^{-2 x^{2}} x^{4}\right ) x}{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 9378 |
\begin{align*}
x^{2}+2 y+4 \left (x +y\right ) y^{\prime }+2 x {y^{\prime }}^{2}+x \left (x +2 y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.017 |
|
| 9379 |
\begin{align*}
z^{\prime }+y^{\prime }+5 y-3 z&=x +{\mathrm e}^{x} \\
y^{\prime }+2 y-z&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 9380 |
\begin{align*}
3 x-y^{\prime }-2 y&=8 t \\
x^{\prime }-2 x+y&=16 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 9381 |
\begin{align*}
\sqrt {y}\, y^{\prime \prime }&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.018 |
|
| 9382 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x^{2}-3\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.018 |
|
| 9383 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}-x_{3}+2 \,{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2}-3 x_{3} \\
x_{3}^{\prime }&=-x_{1}+x_{2}+2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| 9384 |
\begin{align*}
y^{\prime }&=y^{2} \\
y \left (3\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| 9385 |
\begin{align*}
y^{\prime }&=y \sin \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| 9386 |
\begin{align*}
y^{\prime \prime }+\frac {8 y^{\prime }}{3 x}-\left (\frac {2}{3 x^{2}}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| 9387 |
\begin{align*}
x^{\prime }&=-2 x+y-11 \\
y^{\prime }&=-5 x+4 y-35 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| 9388 |
\begin{align*}
x_{1}^{\prime }&=1-x_{2}+x_{3} \\
x_{2}^{\prime }&=2 x_{2}+t \\
x_{3}^{\prime }&=-2 x_{1}-x_{2}+3 x_{3}+{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| 9389 |
\begin{align*}
y^{\prime }&=\left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.020 |
|
| 9390 |
\begin{align*}
{\mathrm e}^{x} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| 9391 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.020 |
|
| 9392 |
\begin{align*}
y^{\prime }+2 y&=3 \,{\mathrm e}^{-2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| 9393 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2}+3 x_{3}+6 x_{4} \\
x_{2}^{\prime }&=3 x_{1}+6 x_{2}+9 x_{3}+18 x_{4} \\
x_{3}^{\prime }&=5 x_{1}+10 x_{2}+15 x_{3}+30 x_{4} \\
x_{4}^{\prime }&=7 x_{1}+14 x_{2}+21 x_{3}+42 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| 9394 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=-2 \delta \left (-2+t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| 9395 |
\begin{align*}
3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| 9396 |
\begin{align*}
4 x^{2} y^{\prime \prime }+y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| 9397 |
\begin{align*}
x^{2} y^{\prime \prime }-6 y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.021 |
|
| 9398 |
\begin{align*}
y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.022 |
|
| 9399 |
\begin{align*}
y^{\prime }&=-y+\operatorname {Heaviside}\left (t -3\right )+\delta \left (t -1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.022 |
|
| 9400 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x +3\right ) y^{\prime }+\left (2 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.023 |
|