| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 2601 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.194 |
|
| 2602 |
\begin{align*}
{y^{\prime }}^{2}-y^{2} x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.194 |
|
| 2603 |
\begin{align*}
x^{2} {y^{\prime }}^{2}-\left (x -y\right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.194 |
|
| 2604 |
\begin{align*}
x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\
y \left (-1\right ) &= -4 \\
y^{\prime }\left (-1\right ) &= -14 \\
y^{\prime \prime }\left (-1\right ) &= -20 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| 2605 |
\begin{align*}
y+3 x^{2}+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| 2606 |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime }&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| 2607 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }-y&=44 \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| 2608 |
\begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+{\mathrm e}^{-y}-\left (x \,{\mathrm e}^{-y}-{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.195 |
|
| 2609 |
\begin{align*}
2 y+y^{\prime }&=2 \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| 2610 |
\begin{align*}
y \left (x +y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| 2611 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= {\frac {81}{10}} \\
y^{\prime }\left (0\right ) &= {\frac {39}{10}} \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| 2612 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.195 |
|
| 2613 |
\begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.195 |
|
| 2614 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+y^{\prime } x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.195 |
|
| 2615 |
\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. |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| 2616 |
\begin{align*}
y^{\prime \prime \prime }+6 y^{\prime \prime }+25 y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 4 \\
y^{\prime \prime }\left (0\right ) &= -24 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| 2617 |
\begin{align*}
y^{\prime \prime }-4 y&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| 2618 |
\begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| 2619 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=2 \,{\mathrm e}^{x}+5 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.196 |
|
| 2620 |
\begin{align*}
x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.196 |
|
| 2621 |
\begin{align*}
x y \sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.196 |
|
| 2622 |
\begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.196 |
|
| 2623 |
\(\left [\begin {array}{cc} 9 & -8 \\ 6 & -5 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.196 |
|
| 2624 |
\(\left [\begin {array}{cc} 11 & -15 \\ 6 & -8 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.196 |
|
| 2625 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.196 |
|
| 2626 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=8 \,{\mathrm e}^{x} \\
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*} |
✓ |
✓ |
✓ |
✓ |
0.196 |
|
| 2627 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+4 x&=4 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -4 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.196 |
|
| 2628 |
\begin{align*}
y^{\prime }&=4 y \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| 2629 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&={\mathrm e}^{x}+\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| 2630 |
\begin{align*}
y^{\prime \prime }+\frac {y}{25}&=\frac {t^{2}}{50} \\
y \left (0\right ) &= -25 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| 2631 |
\begin{align*}
\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.197 |
|
| 2632 |
\begin{align*}
4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| 2633 |
\begin{align*}
\left (1-x \right ) x^{2} y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.197 |
|
| 2634 |
\(\left [\begin {array}{cc} 6 & -10 \\ 2 & -3 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.197 |
|
| 2635 |
\begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=4 t \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -2 \\
y^{\prime \prime }\left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| 2636 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| 2637 |
\begin{align*}
y^{\prime \prime }+10 y^{\prime }+25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| 2638 |
\begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+30 y^{\prime \prime }-56 y^{\prime }+49 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
y^{\prime \prime }\left (0\right ) &= -1 \\
y^{\prime \prime \prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| 2639 |
\begin{align*}
y^{\prime }+y&=3 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| 2640 |
\begin{align*}
y^{\prime \prime \prime }&=f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| 2641 |
\begin{align*}
y^{\prime }+3 y&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| 2642 |
\begin{align*}
e i u^{\prime \prime \prime \prime }&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| 2643 |
\begin{align*}
y^{\prime \prime }+4 y&=\sin \left (3 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| 2644 |
\begin{align*}
y^{\prime \prime }+4 y&=32 \cos \left (2 t \right ) t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| 2645 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=\cos \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.198 |
|
| 2646 |
\begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.198 |
|
| 2647 |
\(\left [\begin {array}{cc} 10 & -6 \\ 12 & -7 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.198 |
|
| 2648 |
\begin{align*}
y^{\prime }+8 y^{\prime \prime } x +4 x^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.198 |
|
| 2649 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.198 |
|
| 2650 |
\begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }+5 y^{\prime }+y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.198 |
|
| 2651 |
\begin{align*}
4 t^{2} y^{\prime \prime }+4 y^{\prime } t +\left (36 t^{2}-1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.198 |
|
| 2652 |
\begin{align*}
y^{\prime }+z&=t \\
z^{\prime }+4 y&=0 \\
\end{align*} With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
z \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.198 |
|
| 2653 |
\begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }&=12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.198 |
|
| 2654 |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=12 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| 2655 |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| 2656 |
\begin{align*}
2 y x +\left (a +x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| 2657 |
\begin{align*}
y^{\prime }+\tan \left (x \right ) y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| 2658 |
\begin{align*}
x^{2} y^{\prime \prime \prime }-y^{\prime \prime } x +\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.199 |
|
| 2659 |
\begin{align*}
-2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| 2660 |
\begin{align*}
y^{\prime \prime }+49 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| 2661 |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| 2662 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| 2663 |
\begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }+y&=x^{5}+2 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| 2664 |
\begin{align*}
y^{\prime \prime \prime }-7 y^{\prime \prime }+14 y^{\prime }-8 y&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| 2665 |
\begin{align*}
y^{\prime }&=t \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| 2666 |
\begin{align*}
t \left (-2+t \right )^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*} Series expansion around \(t=2\). |
✗ |
✗ |
✓ |
✗ |
0.200 |
|
| 2667 |
\begin{align*}
y^{\prime \prime }-x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.200 |
|
| 2668 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.200 |
|
| 2669 |
\begin{align*}
2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.200 |
|
| 2670 |
\begin{align*}
16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.200 |
|
| 2671 |
\begin{align*}
{y^{\prime }}^{2}+y \left (-x +y\right ) y^{\prime }-x y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.200 |
|
| 2672 |
\begin{align*}
x \left (a y^{\prime }+b y^{\prime \prime }+c y^{\prime \prime \prime }+e y^{\prime \prime \prime \prime }\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.200 |
|
| 2673 |
\(\left [\begin {array}{cc} 7 & -6 \\ 12 & -10 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.200 |
|
| 2674 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{2}-1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.200 |
|
| 2675 |
\begin{align*}
{y^{\prime }}^{2}-y^{\prime }-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.200 |
|
| 2676 |
\begin{align*}
x y^{\prime \prime \prime }&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.200 |
|
| 2677 |
\begin{align*}
y^{\prime \prime }+16 y&=t \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.200 |
|
| 2678 |
\begin{align*}
y^{\left (6\right )}+y^{\prime \prime \prime \prime }&=-24 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.200 |
|
| 2679 |
\begin{align*}
y^{\prime \prime }-a x y^{\prime }+a^{2} \left (x -1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.200 |
|
| 2680 |
\begin{align*}
3 y^{2} x^{2}+\left (2 x^{3} y+4 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.200 |
|
| 2681 |
\begin{align*}
y^{\left (5\right )}+2 y^{\prime \prime \prime \prime }&=x \\
y \left (0\right ) &= 0 \\
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 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.200 |
|
| 2682 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y&=\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.200 |
|
| 2683 |
\begin{align*}
y^{\prime \prime }-3 y&=4 t^{2} \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.200 |
|
| 2684 |
\begin{align*}
y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.201 |
|
| 2685 |
\begin{align*}
2 y-3 x +y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.201 |
|
| 2686 |
\begin{align*}
x^{2} y^{\prime \prime \prime }-3 y^{\prime \prime } x +3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.201 |
|
| 2687 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=0 \\
y \left (0\right ) &= 11 \\
y^{\prime }\left (0\right ) &= 28 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.201 |
|
| 2688 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.201 |
|
| 2689 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.201 |
|
| 2690 |
\begin{align*}
x^{\prime }+y^{\prime }+2 y&=\sin \left (t \right ) \\
x^{\prime }+y^{\prime }-x-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.201 |
|
| 2691 |
\begin{align*}
y^{\prime \prime \prime \prime }&=\frac {1}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.201 |
|
| 2692 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=3 \sin \left (x \right ) {\mathrm e}^{-x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.201 |
|
| 2693 |
\begin{align*}
y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }&=x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.201 |
|
| 2694 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=3 \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.201 |
|
| 2695 |
\begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime }&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.201 |
|
| 2696 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=50 \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.201 |
|
| 2697 |
\begin{align*}
y^{\prime \prime }&=y \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.202 |
|
| 2698 |
\begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&={\mathrm e}^{2 x}-4 \,{\mathrm e}^{x}-2 \cos \left (x \right )+4 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.202 |
|
| 2699 |
\begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.202 |
|
| 2700 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.202 |
|