| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 8601 |
\begin{align*}
y^{2}-3 y x -2 x^{2}+\left (y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| 8602 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| 8603 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| 8604 |
\begin{align*}
y^{\prime \prime }-\left (1+2 \tan \left (x \right )^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.433 |
|
| 8605 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| 8606 |
\begin{align*}
\left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+t y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| 8607 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+20 y&=2 t \,{\mathrm e}^{-2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| 8608 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=9 \,{\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| 8609 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }-2 y&=8 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| 8610 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{x}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| 8611 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| 8612 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| 8613 |
\begin{align*}
y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| 8614 |
\begin{align*}
y_{1}^{\prime }&=2 y_{1}-5 y_{2} \\
y_{2}^{\prime }&=y_{1}-2 y_{2} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| 8615 |
\begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (2 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| 8616 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| 8617 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x +2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| 8618 | \begin{align*}
\left (2+x \right ) y^{\prime \prime }+y^{\prime } x +3 y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.434 |
|
| 8619 |
\begin{align*}
\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y&=0 \\
y \left (-1\right ) &= 3 \\
y^{\prime }\left (-1\right ) &= -3 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| 8620 |
\begin{align*}
y^{\prime \prime }-y&=10 \,{\mathrm e}^{2 x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| 8621 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1} \\
x_{2}^{\prime }&=x_{1}-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=-x_{1}+x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| 8622 |
\begin{align*}
y^{\prime \prime }+y&=t -\operatorname {Heaviside}\left (-1+t \right ) \left (-1+t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| 8623 |
\begin{align*}
y+\left (b x +a \right )^{4} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.434 |
|
| 8624 |
\begin{align*}
\left (-2 x^{2}+1\right ) y+4 x^{3} \left (2 x^{2}+1\right ) y^{\prime }+4 x^{6} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.434 |
|
| 8625 |
\begin{align*}
2 y^{\prime \prime \prime } y^{\prime }&=2 {y^{\prime \prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.434 |
|
| 8626 |
\begin{align*}
y&=-y^{\prime } x +x^{4} {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| 8627 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| 8628 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{2}-1} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| 8629 |
\begin{align*}
x^{\prime }&=-4 x+y \\
y^{\prime }&=2 x-3 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| 8630 |
\begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+\left (x^{2}+x -6\right ) y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| 8631 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \left (2 \cos \left (x \right )+\sin \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| 8632 |
\begin{align*}
x^{\prime \prime }-3 x^{\prime }+2 x&=3 \,{\mathrm e}^{t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| 8633 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=\frac {{\mathrm e}^{x}}{x^{3}} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
y^{\prime \prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| 8634 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x}-{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| 8635 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.434 |
|
| 8636 |
\begin{align*}
y^{\prime \prime }-8 y^{\prime }+25 y&=104 \sin \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| 8637 | \begin{align*}
y^{\prime }+4 y&=\delta \left (t -3\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. | ✓ | ✓ | ✓ | ✓ | 0.434 |
|
| 8638 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8639 |
\begin{align*}
y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=\sin \left (3 x \right )+x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8640 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {2 \,{\mathrm e}^{-3 x}}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.435 |
|
| 8641 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8642 |
\begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2} \\
y_{2}^{\prime }&=y_{1}-y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8643 |
\begin{align*}
y^{\prime } x&=\sqrt {a^{2}-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8644 |
\begin{align*}
y {y^{\prime }}^{2}&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8645 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=4 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8646 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x^{5}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8647 |
\begin{align*}
p \left (1+p \right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8648 |
\begin{align*}
y^{\prime \prime } x +\left (x^{3}+1\right ) y^{\prime }+b x y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8649 |
\begin{align*}
\left (2+x \right ) y^{\prime \prime }+3 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8650 |
\begin{align*}
y^{\prime \prime }&=x {y^{\prime }}^{2} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8651 |
\(\left [\begin {array}{ccccc} 2 & 1 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 & 0 \\ 0 & 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & 2 & 1 \\ 0 & 0 & 0 & 0 & 2 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.435 |
|
| 8652 |
\begin{align*}
x^{4} y^{\prime \prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8653 |
\begin{align*}
x^{\prime }&=-x-2 y \\
y^{\prime }&=5 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8654 |
\begin{align*}
x^{\prime }&=3 x+4 y \\
y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8655 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8656 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=8 \,{\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8657 | \begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=10 \cos \left (x \right ) {\mathrm e}^{-2 x} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.435 |
|
| 8658 |
\begin{align*}
x^{\prime }+3 x+4 y&=0 \\
y^{\prime }+2 x+5 y&=0 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8659 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=x \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8660 |
\begin{align*}
x^{\prime \prime }-3 x^{\prime }+2 x&=0 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8661 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| 8662 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {4 \,{\mathrm e}^{x} \ln \left (x \right )}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 8663 |
\begin{align*}
\left (y^{2} x^{2}+1\right ) y+\left (y^{2} x^{2}-1\right ) x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 8664 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\delta \left (-1+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 8665 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 8666 |
\begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=2 x-4 y \\
z^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 8667 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 8668 |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }+12 y&=-2 t^{3} {\mathrm e}^{4 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 8669 |
\begin{align*}
y^{\prime \prime }-y&=x +\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 8670 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 8671 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 8672 |
\begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=3 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 8673 |
\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 \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 8674 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| 8675 |
\begin{align*}
2 y^{\prime \prime }&={y^{\prime }}^{3} \sin \left (2 x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.436 |
|
| 8676 | \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=9 x^{2} \\
y \left (1\right ) &= -7 \\
y^{\prime }\left (1\right ) &= -11 \\
y^{\prime \prime }\left (1\right ) &= -5 \\
y^{\prime \prime \prime }\left (1\right ) &= 6 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.437 |
|
| 8677 |
\begin{align*}
x_{1}^{\prime }&=-x_{2} \\
x_{2}^{\prime }&=8 x_{1}-6 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 8678 |
\begin{align*}
x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 8679 |
\begin{align*}
a^{2} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 8680 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 8681 |
\begin{align*}
\left (x^{2}-2 x \right ) y^{\prime \prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 8682 |
\begin{align*}
2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.437 |
|
| 8683 |
\begin{align*}
x^{\prime }&=-x+4 y \\
y^{\prime }&=2 x-3 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 8684 |
\begin{align*}
y^{\prime \prime }-y^{\prime }+\left (\frac {1}{4}+4 \pi ^{2}\right ) y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 8685 |
\begin{align*}
x^{\prime }&=-5 x+4 y \\
y^{\prime }&=2 x+2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 8686 |
\begin{align*}
y^{\prime }&=y^{3}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 8687 |
\begin{align*}
y^{\prime \prime }+4 y&=g \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 8688 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 8689 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 8690 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 8691 |
\begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 8692 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 8693 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+{\mathrm e}^{x} y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 8694 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| 8695 | \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=25 \,{\mathrm e}^{2 t} t \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.437 |
|
| 8696 |
\begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (-2 x^{2}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| 8697 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-4 x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| 8698 |
\begin{align*}
4 x^{4} y^{\prime \prime \prime \prime }+24 x^{3} y^{\prime \prime \prime }+23 x^{2} y^{\prime \prime }-y^{\prime } x +y&=6 x \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 0 \\
y^{\prime \prime }\left (1\right ) &= 4 \\
y^{\prime \prime \prime }\left (1\right ) &= -{\frac {37}{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| 8699 |
\begin{align*}
x^{\prime }+2 x-y&=0 \\
x+y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| 8700 |
\begin{align*}
x^{3} y^{\prime \prime }&=b x +a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.438 |
|