| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10601 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 10602 |
\begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+37 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 10603 |
\begin{align*}
y^{\prime \prime }-2 x y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 10604 |
\begin{align*}
x^{\prime }+y^{\prime }&=y \\
x^{\prime }-y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 10605 |
\begin{align*}
y^{\prime \prime }+y&=2 \cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| 10606 |
\begin{align*}
y^{\prime \prime }+9 y&=2 \sec \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 10607 |
\begin{align*}
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 10608 |
\begin{align*}
a \cos \left (x \right ) y-\sin \left (x \right ) y^{2}+\left (b \cos \left (x \right ) y-x \sin \left (x \right ) y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.806 |
|
| 10609 |
\begin{align*}
2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 10610 |
\begin{align*}
\left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.806 |
|
| 10611 |
\begin{align*}
9 y^{\prime \prime }+6 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 10612 |
\begin{align*}
y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
y^{\prime \prime }\left (0\right ) &= 5 \\
y^{\prime \prime \prime }\left (0\right ) &= 19 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 10613 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=1-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 10614 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=4+x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 10615 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.806 |
|
| 10616 |
\begin{align*}
y^{\prime \prime }&=3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 10617 |
\begin{align*}
y^{\prime \prime }+9 y&=\cos \left (3 x \right )-\sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 10618 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-x}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 10619 |
\begin{align*}
2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| 10620 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=3 x_{1}-x_{2}+5 \,{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 10621 |
\begin{align*}
\left (x -2 y\right ) y^{\prime }+2 x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 10622 |
\begin{align*}
x^{\prime }+y-t^{2}+6 t +1&=0 \\
-x+y^{\prime }&=-3 t^{2}+3 t +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 10623 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=8 \,{\mathrm e}^{2 t}-5 \,{\mathrm e}^{t} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 10624 |
\begin{align*}
2 x y^{\prime } y^{\prime \prime }&=-1+{y^{\prime }}^{2} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= \sqrt {3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 10625 |
\begin{align*}
y^{\prime \prime }+4 y&=4 \cos \left (t \right )-\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 10626 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (x^{3}+x^{2}+x \right ) y^{\prime }+\left (1+4 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| 10627 |
\begin{align*}
t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 10628 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 10629 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (x +4\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 10630 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 10631 |
\begin{align*}
y^{\prime \prime }+16 y&=\tan \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 10632 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 10633 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 10634 |
\begin{align*}
y^{\prime }&=x \\
x^{\prime }&=-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 10635 |
\begin{align*}
y^{\prime \prime }&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 10636 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y&=0 \\
\end{align*}
Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| 10637 |
\begin{align*}
y^{\prime \prime }-x -3 y x&=0 \\
y \left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.808 |
|
| 10638 |
\begin{align*}
x^{2} \ln \left (x \right )^{2} y^{\prime \prime }-x \ln \left (x \right ) y^{\prime }+\left (1+\ln \left (x \right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.808 |
|
| 10639 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 10640 |
\begin{align*}
x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 10641 |
\begin{align*}
\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.809 |
|
| 10642 |
\begin{align*}
y^{\prime \prime }&=a \sqrt {1+{y^{\prime }}^{2}}+b \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.809 |
|
| 10643 |
\begin{align*}
b y+a y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.809 |
|
| 10644 |
\begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 10645 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 10646 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=4 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 10647 |
\begin{align*}
4 x y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| 10648 |
\begin{align*}
3 y^{\prime \prime }-2 y^{\prime }+4 y&=0 \\
y \left (2\right ) &= 1 \\
y^{\prime }\left (2\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| 10649 |
\begin{align*}
2 a^{2} y-a^{2} y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=\sinh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| 10650 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime \prime }-x y^{\prime }+2 x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| 10651 |
\begin{align*}
x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| 10652 |
\begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=5 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| 10653 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (x -9\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.810 |
|
| 10654 |
\begin{align*}
w^{\prime }+y&=\sin \left (t \right ) \\
y^{\prime }-z&={\mathrm e}^{t} \\
w+y+z^{\prime }&=1 \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 1 \\
w \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.810 |
|
| 10655 |
\begin{align*}
x^{\prime \prime }+4 x&=f \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.811 |
|
| 10656 |
\begin{align*}
y^{\prime }&=\left (-1+y\right )^{2}+\frac {1}{100} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
0.811 |
|
| 10657 |
\begin{align*}
\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.811 |
|
| 10658 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.811 |
|
| 10659 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}+3 \,{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=9 x_{1}-3 x_{2}+{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.811 |
|
| 10660 |
\begin{align*}
\sqrt {x}\, y^{\prime \prime }&=y^{{3}/{2}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.812 |
|
| 10661 |
\begin{align*}
y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\
y \left (-1\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.812 |
|
| 10662 |
\begin{align*}
x^{\prime }&=\left (x-1\right )^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.812 |
|
| 10663 |
\begin{align*}
y^{2}&=a^{2} \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| 10664 |
\begin{align*}
x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| 10665 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 y+z \\
z^{\prime }&=x+3 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| 10666 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x}+15 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| 10667 |
\begin{align*}
x^{\prime \prime }+100 x&=225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \\
x \left (0\right ) &= 375 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| 10668 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| 10669 |
\begin{align*}
3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| 10670 |
\begin{align*}
2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| 10671 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (x^{2}-2 x \right ) y^{\prime }-\left (3 x +2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.813 |
|
| 10672 |
\begin{align*}
y^{\prime \prime }-\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+f \left (x \right ) y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.813 |
|
| 10673 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| 10674 |
\begin{align*}
y_{1}^{\prime }&=2 y_{1}-3 y_{2}+4 x -2 \\
y_{2}^{\prime }&=y_{1}-2 y_{2}+3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| 10675 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| 10676 |
\begin{align*}
3 t^{2}-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| 10677 |
\begin{align*}
x^{\prime }&=y+z \\
y^{\prime }&=x+z \\
z^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| 10678 |
\begin{align*}
y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y&={\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.813 |
|
| 10679 |
\begin{align*}
y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.813 |
|
| 10680 |
\begin{align*}
y^{\prime \prime }+y&=x \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| 10681 |
\begin{align*}
y^{\prime \prime }-y&=x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| 10682 |
\begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime \prime }+2 \left (2 x -a -b \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.813 |
|
| 10683 |
\begin{align*}
y^{\prime \prime }+3 y&=-x^{6}+x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| 10684 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=5 x_{1}+2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| 10685 |
\begin{align*}
{y^{\prime }}^{2} x +\left (x -y\right ) y^{\prime }+1-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.814 |
|
| 10686 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&={\mathrm e}^{x} x^{2}+3 x \,{\mathrm e}^{2 x}+5 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| 10687 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2}-x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}+3 x_{3} \\
x_{3}^{\prime }&=3 x_{1}-4 x_{2}-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| 10688 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+\sqrt {3}\, x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=\sqrt {3}\, x_{1}-x_{2}+\sqrt {3}\, {\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| 10689 |
\begin{align*}
4 {y^{\prime }}^{2} x^{2} \left (x -1\right )-4 y^{\prime } x y \left (4 x -3\right )+\left (16 x -9\right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| 10690 |
\begin{align*}
y^{\prime \prime }-9 y&={\mathrm e}^{3 x}+\sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| 10691 |
\begin{align*}
-4 y-3 y^{\prime }+y^{\prime \prime }&=10 \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| 10692 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{x} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| 10693 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{2} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.815 |
|
| 10694 |
\begin{align*}
x^{\prime \prime }+x^{\prime }-2 x&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| 10695 |
\begin{align*}
y^{\prime \prime }-3&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| 10696 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+\left (2 x -1\right ) y&=0 \\
y \left (-1\right ) &= 2 \\
y^{\prime }\left (-1\right ) &= -2 \\
\end{align*}
Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| 10697 |
\begin{align*}
y^{\prime \prime }-y&=\frac {2}{\sqrt {1-{\mathrm e}^{-2 x}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| 10698 |
\(\left [\begin {array}{cccc} -2 & 1 & 0 & 0 \\ 1 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.815 |
|
| 10699 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.816 |
|
| 10700 |
\begin{align*}
4 y+y^{\prime \prime }&=12 \cos \left (x \right )^{2} \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.816 |
|