| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 8301 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| 8302 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=6 x +4 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| 8303 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| 8304 |
\begin{align*}
x y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| 8305 |
\begin{align*}
a x {y^{\prime }}^{2}-\left (a y+b x -a -b \right ) y^{\prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.611 |
|
| 8306 |
\begin{align*}
x^{4} y^{\prime \prime }+a^{2} y^{n}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.611 |
|
| 8307 |
\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. |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| 8308 |
\begin{align*}
y^{\prime \prime }+9 y&={\mathrm e}^{-2 t} \\
y \left (0\right ) &= -{\frac {2}{13}} \\
y^{\prime }\left (0\right ) &= {\frac {1}{13}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| 8309 |
\begin{align*}
y^{\prime \prime }+4 y&=2 \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| 8310 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| 8311 |
\begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=17 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| 8312 |
\begin{align*}
x y^{\prime \prime }+\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| 8313 |
\begin{align*}
y_{1}^{\prime }&=y_{1}+2 y_{2} \\
y_{2}^{\prime }&=-4 y_{1}+5 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 8314 |
\begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&={\mathrm e}^{\frac {x}{2}} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 8315 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=x^{2} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 8316 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=\sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 8317 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+13 x_{2} \\
x_{2}^{\prime }&=-x_{1}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 8318 |
\begin{align*}
x^{\prime }-2 x-y&=2 \,{\mathrm e}^{t} \\
y^{\prime }-2 y-4 z&=4 \,{\mathrm e}^{2 t} \\
x-z^{\prime }-z&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 9 \\
y \left (0\right ) &= 3 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 8319 |
\begin{align*}
{y^{\prime }}^{2} x^{2}&=\left (x -y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 8320 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+3 x&={\mathrm e}^{-3 t} \\
x \left (0\right ) &= {\frac {1}{2}} \\
x^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 8321 |
\begin{align*}
x^{\prime }&=-6 x+2 y \\
y^{\prime }&=-3 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 8322 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 8323 |
\begin{align*}
y^{\prime \prime }+y&=x^{2}+x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 8324 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 8325 |
\begin{align*}
y^{\prime \prime }&=2 y y^{\prime } \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.612 |
|
| 8326 |
\begin{align*}
4 y+y^{\prime \prime }&=24 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 8327 |
\begin{align*}
4 y^{\prime \prime }-12 y^{\prime }+9 y&=x \,{\mathrm e}^{\frac {3 x}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 8328 |
\begin{align*}
y^{\prime \prime }-\left (x -2\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 8329 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}+1 \\
x_{2}^{\prime }&=x_{1}+t \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -{\frac {1}{2}} \\
x_{2} \left (0\right ) &= -{\frac {1}{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 8330 |
\begin{align*}
y^{\prime }+2 z&=y \\
z^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 8331 |
\begin{align*}
y^{\prime \prime }+y&=2 \cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 8332 |
\begin{align*}
x^{\prime }&=-3 x+\alpha y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| 8333 |
\begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=x+2 y-{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| 8334 |
\begin{align*}
t \left (2-t \right ) y^{\prime \prime }-6 \left (t -1\right ) y^{\prime }-4 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*}
Series expansion around \(t=1\). |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| 8335 |
\begin{align*}
f^{\prime \prime }+8 f^{\prime }+12 f&=12 \,{\mathrm e}^{-4 t} \\
f \left (0\right ) &= 0 \\
f^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| 8336 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {25}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.613 |
|
| 8337 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\left (24 x^{2}+2\right ) {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| 8338 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\left (x^{2}+x \right ) {\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| 8339 |
\begin{align*}
y&=2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.613 |
|
| 8340 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| 8341 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{x}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| 8342 |
\begin{align*}
y^{\prime \prime }-4 y&=2+{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| 8343 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=4 x^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| 8344 |
\begin{align*}
x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.613 |
|
| 8345 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y&=\left (x^{2}-x +1\right ) {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.614 |
|
| 8346 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| 8347 |
\begin{align*}
\cos \left (x \right ) \cos \left (y\right )-2 \sin \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| 8348 |
\begin{align*}
x^{\prime \prime }&=\frac {4 x}{t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| 8349 |
\begin{align*}
y^{\prime }&=y^{2}-2 y+1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| 8350 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| 8351 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=x^{2}+2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| 8352 |
\begin{align*}
x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }&=0 \\
y \left (2\right ) &= 5 \\
y^{\prime }\left (2\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| 8353 |
\begin{align*}
y^{\prime \prime }-y&=\frac {1}{1+{\mathrm e}^{x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| 8354 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+12 y&=0 \\
y \left (2\right ) &= 0 \\
y^{\prime }\left (2\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| 8355 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 8356 |
\begin{align*}
y^{\prime \prime }+4 y&=\sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 8357 |
\begin{align*}
\left (x^{2}-x +1\right ) y^{\prime \prime }-\left (1-4 x \right ) y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 8358 |
\begin{align*}
y^{\prime \prime }-y&=x^{2} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 8359 |
\begin{align*}
x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.615 |
|
| 8360 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 8361 |
\begin{align*}
\left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 8362 |
\begin{align*}
2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=1 \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.615 |
|
| 8363 |
\begin{align*}
3 y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+\sin \left (y\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.615 |
|
| 8364 |
\begin{align*}
x^{2} y^{\prime \prime }+a \left ({\mathrm e}^{y}-1\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.615 |
|
| 8365 |
\begin{align*}
\frac {x^{\prime \prime }}{2}+\frac {5 x^{\prime }}{6}+\frac {2 x}{9}&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 8366 |
\begin{align*}
v^{\prime }&=-v^{2}-2 v-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 8367 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=10 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 8368 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+9 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 8369 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2} \\
x_{2}^{\prime }&=-14 x_{1}-5 x_{2}+x_{3} \\
x_{3}^{\prime }&=15 x_{1}+5 x_{2}-2 x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 5 \\
x_{2} \left (0\right ) &= 5 \\
x_{3} \left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 8370 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=25 x^{2}+12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 8371 |
\begin{align*}
{y^{\prime }}^{3}-\left (y+2 x -{\mathrm e}^{x -y}\right ) {y^{\prime }}^{2}+\left (2 y x -2 x \,{\mathrm e}^{x -y}-y \,{\mathrm e}^{x -y}\right ) y^{\prime }+2 x y \,{\mathrm e}^{x -y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 8372 |
\begin{align*}
\left (-x +3\right ) y^{\prime \prime }-\left (9-4 x \right ) y^{\prime }+\left (6-3 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.615 |
|
| 8373 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\sin \left ({\mathrm e}^{-x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 8374 |
\begin{align*}
x^{\prime }&=-2 x+\frac {5 y}{7} \\
y^{\prime }&=7 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| 8375 |
\begin{align*}
a \,x^{3} y^{\prime \prime \prime }+b \,x^{2} y^{\prime \prime }+c x y^{\prime }+d y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.616 |
|
| 8376 |
\begin{align*}
x_{1}^{\prime }&=-13 x_{1}+40 x_{2}-48 x_{3} \\
x_{2}^{\prime }&=-8 x_{1}+23 x_{2}-24 x_{3} \\
x_{3}^{\prime }&=3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 8377 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 8378 |
\begin{align*}
y^{\prime \prime }+4 y&=6+t^{2}+{\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 8379 |
\begin{align*}
y^{\prime }+2 y-y^{2}&=-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 8380 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+3 x_{3} \\
x_{2}^{\prime }&=6 x_{1}+4 x_{2}+6 x_{3} \\
x_{3}^{\prime }&=-5 x_{1}-2 x_{2}-4 x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= -2 \\
x_{3} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 8381 |
\begin{align*}
y^{\prime \prime \prime }-y&=5 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 8382 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=6 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 8383 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 x}}{x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 8384 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 8385 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 8386 |
\begin{align*}
y_{1}^{\prime }&=-y_{2} \\
y_{2}^{\prime }-2 y_{2}&=y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 8387 |
\begin{align*}
y^{\prime \prime }-4 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 8388 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| 8389 |
\begin{align*}
x_{1}^{\prime }&=25 x_{1}+12 x_{2} \\
x_{2}^{\prime }&=-18 x_{1}-5 x_{2} \\
x_{3}^{\prime }&=6 x_{1}+6 x_{2}+13 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 8390 |
\begin{align*}
x^{\prime \prime }+5 x^{\prime }+6 x&=\cos \left (t \right ) \\
x \left (0\right ) &= {\frac {1}{10}} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 8391 |
\begin{align*}
y+y^{\prime }&={\mathrm e}^{-3 t} \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 8392 |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+10 y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 3 \\
y^{\prime \prime }\left (0\right ) &= 8 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 8393 |
\begin{align*}
y^{\prime \prime }+49 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 8394 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=4 t^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 8395 |
\begin{align*}
{y^{\prime }}^{2} x&={\mathrm e}^{\frac {1}{y^{\prime }}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.617 |
|
| 8396 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=2 \,{\mathrm e}^{x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \\
y \left (\pi \right ) &= \pi \,{\mathrm e}^{\pi } \\
y^{\prime }\left (\pi \right ) &= {\mathrm e}^{\pi } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 8397 |
\begin{align*}
y^{\prime }&=2 x +\cos \left (y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| 8398 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.617 |
|
| 8399 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| 8400 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}-x_{2} \\
x_{2}^{\prime }&=x_{1}-4 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.618 |
|