| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12301 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (2 x^{2}+a \right ) y^{\prime }}{x \left (x^{2}+a \right )}-\frac {b y}{x^{2} \left (x^{2}+a \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.990 |
|
| 12302 |
\begin{align*}
y^{\prime \prime }&=\frac {y^{\prime }}{x}-\frac {a y}{x^{6}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.990 |
|
| 12303 |
\begin{align*}
x^{\prime }&=-2 y \\
y^{\prime }&=-4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.990 |
|
| 12304 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.990 |
|
| 12305 |
\begin{align*}
\left (x^{2}+x \right ) y^{\prime \prime }+\left (x -2\right ) y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.990 |
|
| 12306 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.990 |
|
| 12307 |
\begin{align*}
-2 y+y^{\prime }&=\operatorname {Heaviside}\left (-2+t \right ) {\mathrm e}^{-2+t} \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.991 |
|
| 12308 |
\begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.991 |
|
| 12309 |
\begin{align*}
\left (y^{2} x^{2}+y x \right ) y+\left (y^{2} x^{2}-1\right ) x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.992 |
|
| 12310 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=\left \{\begin {array}{cc} x & 0\le x <1 \\ -x & 1\le x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.992 |
|
| 12311 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }-7 x^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.992 |
|
| 12312 |
\begin{align*}
y^{\prime }-y^{3}&=8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.992 |
|
| 12313 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-2 x_{2}+\delta \left (t -\pi \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| 12314 |
\begin{align*}
\cos \left (x \right ) \cos \left (y\right )^{2}-\sin \left (x \right ) \sin \left (2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| 12315 |
\begin{align*}
\sqrt {x}\, y^{\prime \prime }+y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| 12316 |
\begin{align*}
\left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2}}{a}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.993 |
|
| 12317 |
\begin{align*}
y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y&={\mathrm e}^{x} \sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.993 |
|
| 12318 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.994 |
|
| 12319 |
\begin{align*}
y^{\prime \prime }+10 y^{\prime }+26 y&=37 \,{\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.994 |
|
| 12320 |
\begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.995 |
|
| 12321 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } t +t^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.995 |
|
| 12322 |
\begin{align*}
y^{\prime }&=x -3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.995 |
|
| 12323 |
\begin{align*}
y^{\prime \prime }+2 z \omega _{n} y^{\prime }+\omega _{n}^{2} y&={\mathrm e}^{c t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.995 |
|
| 12324 |
\begin{align*}
y x -1+\left (x^{2}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.996 |
|
| 12325 |
\begin{align*}
4 x^{2} y^{\prime \prime }-x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.996 |
|
| 12326 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.996 |
|
| 12327 |
\begin{align*}
\left (-x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.996 |
|
| 12328 |
\begin{align*}
y y^{\prime \prime }-a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.996 |
|
| 12329 |
\begin{align*}
x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.996 |
|
| 12330 |
\begin{align*}
y^{\prime \prime }&=f \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.996 |
|
| 12331 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1} \\
x_{2}^{\prime }&=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4} \\
x_{3}^{\prime }&=5 x_{3} \\
x_{4}^{\prime }&=-21 x_{3}-2 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| 12332 |
\begin{align*}
y y^{\prime } x +y^{2}-\sin \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| 12333 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| 12334 |
\begin{align*}
x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.997 |
|
| 12335 |
\begin{align*}
4 x^{\prime }+2 y^{\prime }+3 x&=E \sin \left (t \right ) \\
4 x+2 x^{\prime }+3 y&=0 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| 12336 |
\begin{align*}
y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.998 |
|
| 12337 |
\begin{align*}
x^{4} y^{\prime \prime }-x \left (x^{2}+2 y\right ) y^{\prime }+4 y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.998 |
|
| 12338 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.998 |
|
| 12339 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }+\left (2-4 x \right ) y^{\prime }-y&=4 x^{2} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.998 |
|
| 12340 |
\begin{align*}
y^{\prime \prime }&=6 \sin \left (3 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.998 |
|
| 12341 |
\begin{align*}
y^{\prime }&=x -y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.999 |
|
| 12342 |
\begin{align*}
x^{\prime }&=2 x-4 y \\
y^{\prime }&=2 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.999 |
|
| 12343 |
\begin{align*}
x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime }&=x^{2} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.999 |
|
| 12344 |
\begin{align*}
-y+y^{\prime }&=10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.999 |
|
| 12345 |
\begin{align*}
y^{\prime \prime }+\left (1-\frac {2}{x^{2}}\right ) y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.999 |
|
| 12346 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-{\mathrm e}^{t} \\
x_{2}^{\prime }&=2 x_{1}-3 x_{2}+2 x_{3}+6 \,{\mathrm e}^{-t} \\
x_{3}^{\prime }&=x_{1}-2 x_{2}+2 x_{3}+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| 12347 |
\begin{align*}
\left (x^{2}+x -2\right ) y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }-\left (6 x^{2}+7 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.000 |
|
| 12348 |
\begin{align*}
-\left (5+4 x \right ) y+32 y^{\prime } x +16 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| 12349 |
\begin{align*}
\left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2}&=4 y^{2} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.000 |
|
| 12350 |
\begin{align*}
y_{1}^{\prime }&=2 y_{1}-5 y_{2}+2 \cos \left (t \right ) \\
y_{2}^{\prime }&=y_{1}-2 y_{2}+\cos \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| 12351 |
\begin{align*}
y^{\prime \prime }+b y^{\prime }+c y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| 12352 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{-2 x} \sin \left ({\mathrm e}^{-x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.001 |
|
| 12353 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.001 |
|
| 12354 |
\begin{align*}
{y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.001 |
|
| 12355 |
\begin{align*}
x^{2}&=a^{2} \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.002 |
|
| 12356 |
\begin{align*}
x^{\prime }&=x+y+z-2 \,{\mathrm e}^{-t} \\
y^{\prime }&=2 x+y-z-2 \,{\mathrm e}^{-t} \\
z^{\prime }&=-3 x+2 y+4 z+3 \,{\mathrm e}^{-t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 12357 |
\begin{align*}
2 y+3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 12358 |
\begin{align*}
-\left (\left (2 n +1\right )^{2}-4 x^{2}\right ) y+4 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 12359 |
\begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 12360 |
\begin{align*}
x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 12361 |
\begin{align*}
x^{\prime }&=-3 y \\
y^{\prime }&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 12362 |
\begin{align*}
y^{\prime }&=y-x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 12363 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 12364 |
\begin{align*}
y^{\prime \prime }+y^{\prime } t +y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.004 |
|
| 12365 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 12366 |
\begin{align*}
y^{\prime }+\cot \left (x \right ) y&=5 \,{\mathrm e}^{\cos \left (x \right )} \\
y \left (\frac {\pi }{2}\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 12367 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{t}+\lambda y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 12368 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{x} \tan \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 12369 |
\begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }+\left (3 x -2\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.004 |
|
| 12370 |
\begin{align*}
-y^{\prime }+y^{\prime \prime } x&=3 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 12371 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }+\left (2-4 x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 12372 |
\begin{align*}
x^{\prime }+2 x+y^{\prime }+y&={\mathrm e}^{-3 t} \\
5 x+y^{\prime }+3 y&=5 \,{\mathrm e}^{-t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 12373 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-5 x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| 12374 |
\begin{align*}
x^{2} \left (x -y\right ) y^{\prime \prime }&=\left (-y+y^{\prime } x \right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.005 |
|
| 12375 |
\begin{align*}
\left (-y^{\prime }+y^{\prime \prime } x \right )^{2}&=1+{y^{\prime \prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.005 |
|
| 12376 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.005 |
|
| 12377 |
\begin{align*}
y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| 12378 |
\begin{align*}
2 x^{2} y^{\prime \prime }+\left (-2 x^{3}+5 x \right ) y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| 12379 |
\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 \(x=3\). |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| 12380 |
\begin{align*}
4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| 12381 |
\begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )&=R^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| 12382 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (1+3 x \right ) y^{\prime }+\left (1-6 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| 12383 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{4} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.006 |
|
| 12384 |
\begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&=4 x \,{\mathrm e}^{-3 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| 12385 |
\begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y&=-{\mathrm e}^{x} \left (\left (4 x^{2}+5 x +9\right ) \cos \left (2 x \right )-\left (-3 x^{2}-5 x +6\right ) \sin \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 12386 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=\sin \left (t \right )+{\mathrm e}^{2 t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 12387 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (t -2 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 12388 |
\begin{align*}
y^{\prime \prime }&=-\frac {a \left (n -1\right ) \sin \left (2 a x \right ) y^{\prime }}{\cos \left (a x \right )^{2}}-\frac {n \,a^{2} \left (\left (n -1\right ) \sin \left (a x \right )^{2}+\cos \left (a x \right )^{2}\right ) y}{\cos \left (a x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.007 |
|
| 12389 |
\begin{align*}
5 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| 12390 |
\begin{align*}
x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| 12391 |
\begin{align*}
y^{\prime \prime }+a y^{\prime }+f \left (x \right ) \sin \left (y\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.008 |
|
| 12392 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| 12393 |
\begin{align*}
4 y+y^{\prime \prime }&=8 \cos \left (2 x \right )-4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| 12394 |
\begin{align*}
x^{\prime }+x+2 y&=1 \\
2 x+y^{\prime }-2 y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| 12395 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| 12396 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| 12397 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| 12398 |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.009 |
|
| 12399 |
\begin{align*}
y^{\prime }&=y \left (-2+y\right ) \left (3+y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| 12400 |
\begin{align*}
x^{\prime }&=x+2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.009 |
|