| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10401 |
\begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.471 |
|
| 10402 |
\begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-x-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.471 |
|
| 10403 |
\begin{align*}
-y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.471 |
|
| 10404 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.472 |
|
| 10405 |
\begin{align*}
x^{\prime \prime }+x^{\prime }-\beta x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.472 |
|
| 10406 |
\begin{align*}
y^{\prime }-\cos \left (a y+b x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.473 |
|
| 10407 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{x} \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.473 |
|
| 10408 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.473 |
|
| 10409 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}-8 \\
x_{2}^{\prime }&=x_{1}+x_{2}+3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| 10410 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}+f \left (x \right ) y^{\prime }-y f^{\prime }\left (x \right )-y^{3}&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
1.474 |
|
| 10411 |
\begin{align*}
x^{\prime \prime }+2 t x^{\prime }-4 x&=1 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.474 |
|
| 10412 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| 10413 |
\begin{align*}
y^{\prime \prime }&={\mathrm e}^{t} \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| 10414 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=2 t^{2}+4 \,{\mathrm e}^{2 t} t +t \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| 10415 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| 10416 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| 10417 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \sec \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| 10418 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=6 x +6 \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| 10419 |
\begin{align*}
g^{\prime \prime }-3 g^{\prime }+2 g&=\delta \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| 10420 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=t^{2} {\mathrm e}^{4 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.475 |
|
| 10421 |
\begin{align*}
\left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+2 y&=x^{2} \left (2+x \right )^{2} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.476 |
|
| 10422 |
\begin{align*}
\left (3 a x +5\right ) y-x \left (a x +5\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.476 |
|
| 10423 |
\begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=2 x-4 y \\
z^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.476 |
|
| 10424 |
\begin{align*}
y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.476 |
|
| 10425 |
\begin{align*}
y^{\prime \prime }-9 y&=-72 x \,{\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.476 |
|
| 10426 |
\begin{align*}
y^{\prime }&=\tan \left (y x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.477 |
|
| 10427 |
\begin{align*}
y^{2} {y^{\prime }}^{3}-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.477 |
|
| 10428 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&={\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. |
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| 10429 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+\left (1-\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.477 |
|
| 10430 |
\begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| 10431 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| 10432 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| 10433 |
\begin{align*}
\left (6-9 x \right ) y-\left (4-5 x \right ) x y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.478 |
|
| 10434 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.478 |
|
| 10435 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=x \,{\mathrm e}^{x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.478 |
|
| 10436 |
\begin{align*}
x^{\prime }&=2 x+2 y \\
y^{\prime }&=-4 x+6 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.478 |
|
| 10437 |
\begin{align*}
x_{1}^{\prime }&=\frac {4 x_{1}}{3}+\frac {4 x_{2}}{3}-\frac {11 x_{3}}{3} \\
x_{2}^{\prime }&=-\frac {16 x_{1}}{3}-\frac {x_{2}}{3}+\frac {14 x_{3}}{3} \\
x_{3}^{\prime }&=3 x_{1}-2 x_{2}-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.478 |
|
| 10438 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.478 |
|
| 10439 |
\begin{align*}
y^{\prime \prime }-y&=x \sin \left (x \right )+\left (x^{2}+1\right ) {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.478 |
|
| 10440 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+8 y&={\mathrm e}^{x} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.478 |
|
| 10441 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.479 |
|
| 10442 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+b \right ) y^{\prime }+a \left (b -1\right ) x^{n -1} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.479 |
|
| 10443 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }&={\mathrm e}^{4 x} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.479 |
|
| 10444 |
\begin{align*}
y^{\prime \prime }-y^{\prime }&={\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.479 |
|
| 10445 |
\begin{align*}
y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (a -1\right ) b +a \,x^{2}+\left (1-a \right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.480 |
|
| 10446 |
\begin{align*}
\left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.480 |
|
| 10447 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+3 \\
\end{align*}
With initial conditions \begin{align*}
x \left (\pi \right ) &= 1 \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.480 |
|
| 10448 |
\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*} |
✓ |
✓ |
✓ |
✓ |
1.481 |
|
| 10449 |
\begin{align*}
{y^{\prime }}^{3}-\left (b x +a \right ) y^{\prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.481 |
|
| 10450 |
\begin{align*}
y^{\prime \prime }+y&=\cot \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.481 |
|
| 10451 |
\begin{align*}
x^{\left (5\right )}+x&=0 \\
x \left (\infty \right ) &= 0 \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
1.481 |
|
| 10452 |
\begin{align*}
x^{\prime }&=x-y-z \\
y^{\prime }&=y+3 z \\
z^{\prime }&=3 y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.481 |
|
| 10453 |
\begin{align*}
y^{\prime \prime }+9 y&=27 t^{3} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.483 |
|
| 10454 |
\begin{align*}
x^{\prime \prime }+t x^{\prime }+x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.483 |
|
| 10455 |
\begin{align*}
2 y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.483 |
|
| 10456 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=4 x^{2}-3 \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.483 |
|
| 10457 |
\begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.484 |
|
| 10458 |
\begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.484 |
|
| 10459 |
\begin{align*}
\left (y^{\prime \prime } x -y^{\prime }\right )^{2}&=1+{y^{\prime \prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.484 |
|
| 10460 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
1.484 |
|
| 10461 |
\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*} |
✓ |
✓ |
✓ |
✓ |
1.484 |
|
| 10462 |
\begin{align*}
y^{\prime \prime }+9 y&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.484 |
|
| 10463 |
\begin{align*}
y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=\left (1+\ln \left (x \right )\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.484 |
|
| 10464 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{-x} \ln \left (x \right )}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.484 |
|
| 10465 |
\begin{align*}
{y^{\prime }}^{3} x -y {y^{\prime }}^{2}+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.485 |
|
| 10466 |
\begin{align*}
y^{\prime }-x&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.485 |
|
| 10467 |
\begin{align*}
4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.485 |
|
| 10468 |
\begin{align*}
4 x^{2} {y^{\prime }}^{2}-4 y y^{\prime } x&=8 x^{3}-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.486 |
|
| 10469 |
\begin{align*}
\left (-1+x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.486 |
|
| 10470 |
\begin{align*}
-\cos \left (x \right ) y-\sin \left (x \right ) y^{\prime }+y^{\prime \prime }&=a -x +x \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.487 |
|
| 10471 |
\begin{align*}
x^{\prime }&=-2 x+5 y \\
y^{\prime }&=-2 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.487 |
|
| 10472 |
\begin{align*}
y^{\prime }+a y^{2}-b \,x^{2 \nu }-c \,x^{\nu -1}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.487 |
|
| 10473 |
\begin{align*}
y^{\prime \prime }&=\frac {\left (a +b \right ) y^{\prime }}{x^{2}}-\frac {\left (\left (a +b \right ) x +a b \right ) y}{x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.487 |
|
| 10474 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y&=x^{2}+\frac {1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.487 |
|
| 10475 |
\begin{align*}
x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.487 |
|
| 10476 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.487 |
|
| 10477 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {15}{8}} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.488 |
|
| 10478 |
\begin{align*}
t^{2} y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.488 |
|
| 10479 |
\begin{align*}
y^{\prime \prime }-y&=\cosh \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.489 |
|
| 10480 |
\begin{align*}
\left (2+x \right )^{2} y^{\prime \prime }+3 \left (2+x \right ) y^{\prime }-3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.489 |
|
| 10481 |
\begin{align*}
x^{\prime }&=4 x+2 y \\
y^{\prime }&=-3 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.489 |
|
| 10482 |
\begin{align*}
4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.490 |
|
| 10483 |
\begin{align*}
y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.490 |
|
| 10484 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +4 \left (x^{4}-1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.490 |
|
| 10485 |
\begin{align*}
t y^{\prime \prime }-\left (1+t \right ) y^{\prime }+y&={\mathrm e}^{2 t} t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.490 |
|
| 10486 |
\begin{align*}
s y^{\prime \prime }+\lambda y&=0 \\
y \left (0\right ) &= 0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.490 |
|
| 10487 |
\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. |
✓ |
✓ |
✓ |
✓ |
1.491 |
|
| 10488 |
\begin{align*}
x^{\prime }&=t \cos \left (t^{2}\right ) \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.491 |
|
| 10489 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.491 |
|
| 10490 |
\begin{align*}
y^{\prime }&={\mathrm e}^{2 t}-1 \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.491 |
|
| 10491 |
\begin{align*}
\left (a +b \cos \left (2 x \right )\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.492 |
|
| 10492 |
\begin{align*}
y-y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=\cos \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.492 |
|
| 10493 |
\begin{align*}
y^{\prime \prime }-12 y^{\prime }+36 y&=3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.492 |
|
| 10494 |
\begin{align*}
x^{\prime }&=y+{\mathrm e}^{t} \\
y^{\prime }&=-2 x+3 y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.492 |
|
| 10495 |
\begin{align*}
y^{\prime \prime }+10 y^{\prime }+25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.492 |
|
| 10496 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+18 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.492 |
|
| 10497 |
\begin{align*}
y^{\prime \prime }-9 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.493 |
|
| 10498 |
\begin{align*}
t^{2} x^{\prime \prime }-2 x&=t^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.493 |
|
| 10499 |
\begin{align*}
y^{\prime \prime }+4 y&=\sin \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.493 |
|
| 10500 |
\begin{align*}
y^{\prime \prime }-2 y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.493 |
|