| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 2401 |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }+x&=t +\delta \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2402 |
\begin{align*}
x^{2} y^{\prime }&=y^{2}+y x -x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2403 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=-{\mathrm e}^{x} \left (7+6 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2404 |
\begin{align*}
-y+y^{\prime }&=6 \cos \left (t \right ) \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2405 |
\begin{align*}
y^{\prime \prime }+4 y&=10 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2406 |
\begin{align*}
y^{\prime \prime }+y&=6 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2407 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=8 \,{\mathrm e}^{t} \sin \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2408 |
\begin{align*}
x^{2} {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2409 |
\begin{align*}
y {y^{\prime }}^{2}+y^{2} y^{\prime \prime }&=b x +a \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.148 |
|
| 2410 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&={\mathrm e}^{x}+\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2411 |
\begin{align*}
3 y^{\prime \prime \prime }+x y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2412 |
\begin{align*}
x^{2} {y^{\prime }}^{2}-3 x y^{\prime } y+2 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2413 |
\begin{align*}
3 \ln \left (x \right ) x^{2}+x^{2}+y+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2414 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2415 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (1-2 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2416 |
\begin{align*}
y^{\prime \prime } x -2 \left (x +1\right ) y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.148 |
|
| 2417 |
\begin{align*}
y^{\prime \prime } x +\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.148 |
|
| 2418 | \begin{align*}
4 x^{2} y^{\prime \prime }-x^{4} {y^{\prime }}^{2}+4 y&=0 \\
\end{align*} | ✗ | ✗ | ✗ | ✗ | 0.148 |
|
| 2419 |
\(\left [\begin {array}{cc} -1 & 4 \\ -1 & 3 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.148 |
|
| 2420 |
\begin{align*}
x^{\prime \prime }-2 x&=1 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2421 |
\begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+37 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2422 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -6 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2423 |
\begin{align*}
y^{\prime \prime \prime \prime }-a^{4} y&=5 a^{4} {\mathrm e}^{a x} \sin \left (a x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2424 |
\begin{align*}
y^{\prime \prime }+4 y&=\cos \left (2 t \right ) \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2425 |
\begin{align*}
y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} {\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2426 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=5 x^{5} {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2427 |
\begin{align*}
8 y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+66 y^{\prime \prime \prime }-41 y^{\prime \prime }-37 y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -14 \\
y^{\prime \prime }\left (0\right ) &= -14 \\
y^{\prime \prime \prime }\left (0\right ) &= 139 \\
y^{\prime \prime \prime \prime }\left (0\right ) &= -{\frac {29}{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2428 |
\begin{align*}
y^{\prime \prime \prime }-13 y^{\prime }+12 y&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| 2429 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.149 |
|
| 2430 |
\begin{align*}
x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.149 |
|
| 2431 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (1-2 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.149 |
|
| 2432 |
\begin{align*}
\left (1-x \right )^{2} x^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.149 |
|
| 2433 |
\begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y-32 \sin \left (2 x \right )+24 \cos \left (2 x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.149 |
|
| 2434 |
\begin{align*}
-3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=3 x^{2}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.149 |
|
| 2435 |
\begin{align*}
x^{\prime \prime }+3 x^{\prime }+2 x&={\mathrm e}^{-4 t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.149 |
|
| 2436 |
\begin{align*}
-y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.149 |
|
| 2437 |
\begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.149 |
|
| 2438 | \begin{align*}
2 y^{\prime }+y&={\mathrm e}^{x} \\
y \left (2\right ) &= \frac {4 \,{\mathrm e}^{2}}{3} \\
\end{align*} Using Laplace transform method. | ✓ | ✓ | ✓ | ✓ | 0.149 |
|
| 2439 |
\begin{align*}
x^{\prime \prime }-6 x^{\prime }+8 x&=2 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| 2440 |
\begin{align*}
y^{\prime \prime }+y&=\delta \left (t -2 \pi \right ) \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| 2441 |
\begin{align*}
x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\
y \left (1\right ) &= k_{0} \\
y^{\prime }\left (1\right ) &= k_{1} \\
y^{\prime \prime }\left (1\right ) &= k_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| 2442 |
\begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| 2443 |
\begin{align*}
\sin \left (y\right )+y \cos \left (x \right )+\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.150 |
|
| 2444 |
\begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=2 \,{\mathrm e}^{-x}+3 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| 2445 |
\begin{align*}
x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (-3 x +4\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.150 |
|
| 2446 |
\begin{align*}
x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| 2447 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.150 |
|
| 2448 |
\begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| 2449 |
\begin{align*}
y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 16 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime \prime }\left (0\right ) &= 0 \\
y^{\left (5\right )}\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| 2450 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| 2451 |
\begin{align*}
x^{\prime \prime \prime \prime }+3 x^{\prime \prime \prime }+2 x^{\prime \prime }&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| 2452 |
\begin{align*}
x^{\prime }+3 y^{\prime }+y&={\mathrm e}^{t} \\
-x+y^{\prime }&=y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| 2453 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=4 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| 2454 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| 2455 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+16 y&=0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| 2456 |
\begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&=1+x \,{\mathrm e}^{x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| 2457 | \begin{align*}
x^{\prime \prime }-x^{\prime }-2 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. | ✓ | ✓ | ✓ | ✓ | 0.151 |
|
| 2458 |
\begin{align*}
x^{\prime \prime }+9 x&=6 \cos \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| 2459 |
\begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| 2460 |
\begin{align*}
y^{\left (5\right )}+y^{\prime \prime \prime \prime }&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| 2461 |
\begin{align*}
2 x^{3}-y^{4}+x y^{3} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| 2462 |
\begin{align*}
\operatorname {a3} y+\operatorname {a2} y^{\prime }+\operatorname {a1} y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| 2463 |
\begin{align*}
y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| 2464 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.151 |
|
| 2465 |
\begin{align*}
y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.151 |
|
| 2466 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.151 |
|
| 2467 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.151 |
|
| 2468 |
\begin{align*}
b x +a y {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.151 |
|
| 2469 |
\(\left [\begin {array}{cc} 7 & 1 \\ -4 & 11 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.151 |
|
| 2470 |
\begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| 2471 |
\begin{align*}
y^{\prime \prime }+9 y&=18 t \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| 2472 |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+4 y&=y^{3} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.151 |
|
| 2473 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| 2474 |
\begin{align*}
y^{\prime \prime \prime \prime }+9 y^{\prime \prime }&=9 \,{\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| 2475 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| 2476 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| 2477 | \begin{align*}
x^{6} y^{\left (6\right )}-12 x^{4} y^{\prime \prime \prime \prime }&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.151 |
|
| 2478 |
\begin{align*}
4 y^{\prime \prime }-3 y^{\prime }-y&=34 \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| 2479 |
\begin{align*}
y^{\prime }+2 y&=3 \,{\mathrm e}^{t} \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| 2480 |
\begin{align*}
t x^{\prime \prime }+\left (3 t -1\right ) x^{\prime }+3 x&=0 \\
x \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.152 |
|
| 2481 |
\begin{align*}
t x^{\prime \prime }-2 x^{\prime }+t x&=0 \\
x \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.152 |
|
| 2482 |
\begin{align*}
y^{\prime \prime }+4 y&=2 \delta \left (t -\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.152 |
|
| 2483 |
\begin{align*}
2 y^{\prime \prime \prime }-7 y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{2 x} \left (17+30 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.152 |
|
| 2484 |
\begin{align*}
x^{2} {y^{\prime }}^{2}-5 x y^{\prime } y+6 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.152 |
|
| 2485 |
\begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=\left (-x^{2}+2\right ) {\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.152 |
|
| 2486 |
\begin{align*}
\cos \left (y\right )-\left (x \sin \left (y\right )-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.152 |
|
| 2487 |
\begin{align*}
y^{2}+y-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.152 |
|
| 2488 |
\begin{align*}
-y-{\mathrm e}^{x} x^{2}+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.152 |
|
| 2489 |
\begin{align*}
{y^{\prime }}^{2}&=4 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.152 |
|
| 2490 |
\begin{align*}
{y^{\prime }}^{2}-y^{2} x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.152 |
|
| 2491 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.152 |
|
| 2492 |
\begin{align*}
y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.152 |
|
| 2493 |
\begin{align*}
2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.152 |
|
| 2494 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.152 |
|
| 2495 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.152 |
|
| 2496 | \begin{align*}
x^{2} {y^{\prime }}^{2}+3 x y^{\prime } y+2 y^{2}&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.152 |
|
| 2497 |
\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. |
✓ |
✓ |
✓ |
✓ |
0.152 |
|
| 2498 |
\begin{align*}
2 y+y^{\prime }&=4 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.152 |
|
| 2499 |
\begin{align*}
y^{\prime \prime }-12 y^{\prime }+45 y&=\delta \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.152 |
|
| 2500 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.152 |
|