| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12701 |
\begin{align*}
x^{2} y^{\prime \prime }-6 y&=\ln \left (x \right ) \\
y \left (1\right ) &= {\frac {1}{6}} \\
y^{\prime }\left (1\right ) &= -{\frac {1}{6}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| 12702 |
\begin{align*}
y_{1}^{\prime }&=3 y_{1}+2 y_{2} \\
y_{2}^{\prime }&=3 y_{2}-2 y_{1} \\
y_{3}^{\prime }&=y_{3} \\
y_{4}^{\prime }&=2 y_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| 12703 |
\begin{align*}
y^{\prime \prime }-9 y&=20 \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 18 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| 12704 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+13 x_{2} \\
x_{2}^{\prime }&=-x_{1}-2 x_{2} \\
x_{3}^{\prime }&=2 x_{3}+4 x_{4} \\
x_{4}^{\prime }&=2 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| 12705 |
\begin{align*}
y^{\prime \prime }-y^{\prime }&={\mathrm e}^{x} \left (x^{2}+10\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| 12706 |
\begin{align*}
y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| 12707 |
\begin{align*}
x^{\prime }&=x^{2}-1 \\
x \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.074 |
|
| 12708 |
\begin{align*}
y^{\prime \prime }-y^{\prime }&=6 x^{5} {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.074 |
|
| 12709 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.074 |
|
| 12710 |
\begin{align*}
x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-y^{\prime } x +y&=x \left (1-\ln \left (x \right )\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.075 |
|
| 12711 |
\begin{align*}
x \left (-x^{2}+1\right ) y^{\prime \prime }+5 \left (-x^{2}+1\right ) y^{\prime }-4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.075 |
|
| 12712 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
1.075 |
|
| 12713 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=27 t \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.075 |
|
| 12714 |
\begin{align*}
t^{2} y^{\prime \prime }+5 y^{\prime } t -5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| 12715 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| 12716 |
\begin{align*}
y y^{\prime \prime }&=y^{2} y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.076 |
|
| 12717 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| 12718 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{3} \cos \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.077 |
|
| 12719 |
\begin{align*}
\left (x -y\right ) y^{\prime \prime }-\left (1+y^{\prime }\right ) \left (1+{y^{\prime }}^{2}\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.077 |
|
| 12720 |
\begin{align*}
y^{\prime }&=\left (x -y\right )^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.077 |
|
| 12721 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.077 |
|
| 12722 |
\begin{align*}
x^{\prime }&=-3 x+5 y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.077 |
|
| 12723 |
\begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2}+y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.078 |
|
| 12724 |
\begin{align*}
2 y+y^{\prime }&=3 x -6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.078 |
|
| 12725 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.078 |
|
| 12726 |
\begin{align*}
y^{\prime \prime }+c y^{\prime }+k y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.078 |
|
| 12727 |
\begin{align*}
y^{\prime \prime } x -\left (x^{2}-x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.078 |
|
| 12728 |
\begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.078 |
|
| 12729 |
\begin{align*}
\left (x^{2}-3 x +1\right ) y^{\prime \prime }-\left (x^{2}-x -2\right ) y^{\prime }+\left (2 x -3\right ) y&=x \left (x^{2}-3 x +1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.078 |
|
| 12730 |
\begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=4 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.078 |
|
| 12731 |
\begin{align*}
y^{\prime }&=\frac {2 \sqrt {-1+y}}{3} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.079 |
|
| 12732 |
\begin{align*}
y y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.079 |
|
| 12733 |
\begin{align*}
\left (t^{2}-t -2\right ) x^{\prime \prime }+\left (1+t \right ) x^{\prime }-\left (-2+t \right ) x&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.079 |
|
| 12734 |
\begin{align*}
y^{\prime \prime }+\cos \left (x \right ) y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.079 |
|
| 12735 |
\begin{align*}
t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| 12736 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{t} \left (t^{2}+1\right ) \sin \left (2 t \right )+3 \,{\mathrm e}^{-t} \cos \left (t \right )+4 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| 12737 |
\begin{align*}
y^{\prime \prime } x&=y^{\prime }+{y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.081 |
|
| 12738 |
\begin{align*}
y^{\prime \prime } x -2 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.081 |
|
| 12739 |
\begin{align*}
-y x -\left (2 x^{2}+1\right ) y^{\prime }+2 y^{\prime \prime } x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.081 |
|
| 12740 |
\begin{align*}
y^{\prime }&=3-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.081 |
|
| 12741 |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y&=g \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.081 |
|
| 12742 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.081 |
|
| 12743 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x \sin \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.082 |
|
| 12744 |
\begin{align*}
x \left (x^{2}+1\right ) y^{\prime \prime }+2 \left (x^{2}-1\right ) y^{\prime }-2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.082 |
|
| 12745 |
\begin{align*}
y^{\prime \prime }&=2 y y^{\prime } \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.082 |
|
| 12746 |
\begin{align*}
x&=\ln \left (y^{\prime }\right )+\sin \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.082 |
|
| 12747 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=1+t^{2}+{\mathrm e}^{-2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.083 |
|
| 12748 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}+26 \sin \left (t \right ) \\
x_{2}^{\prime }&=3 x_{1}+4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| 12749 |
\begin{align*}
x \left (x -2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| 12750 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| 12751 |
\begin{align*}
y^{\prime }&=200 y-2 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| 12752 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+18 y&=2 \operatorname {Heaviside}\left (\pi -t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| 12753 |
\begin{align*}
x^{4} \left (x^{2}-4\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+\left (x^{2}-3 x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| 12754 |
\begin{align*}
t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| 12755 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 12756 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}-x_{2}+3 x_{3} \\
x_{3}^{\prime }&=-x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 12757 |
\begin{align*}
3 x^{\prime }+2 x+y^{\prime }-6 y&=5 \,{\mathrm e}^{t} \\
4 x^{\prime }+2 x+y^{\prime }-8 y&=5 \,{\mathrm e}^{t}+2 t -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 12758 |
\begin{align*}
2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 12759 |
\begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }&=18 x^{2}+16 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{3 x}-9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 12760 |
\begin{align*}
x^{\prime }&=-7 x+6 y+6 \,{\mathrm e}^{-t} \\
y^{\prime }&=-12 x+5 y+37 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 12761 |
\begin{align*}
x^{\prime }+2 x&=6 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 12762 |
\begin{align*}
y^{\prime }&={\mathrm e}^{y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 12763 |
\begin{align*}
{\mathrm e}^{x} \left (y^{3}+x y^{3}+1\right )+3 y^{2} \left (x \,{\mathrm e}^{x}-6\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| 12764 |
\begin{align*}
y^{\prime \prime } x +x^{3} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| 12765 |
\begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| 12766 |
\begin{align*}
a^{2} {y^{\prime \prime }}^{2}-2 a x y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.086 |
|
| 12767 |
\begin{align*}
y^{\prime }+\left (2+x \right ) y^{\prime \prime }+\left (2+x \right )^{2} y^{\prime \prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.086 |
|
| 12768 |
\begin{align*}
x^{\prime }+x&=\sin \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| 12769 |
\begin{align*}
y^{\prime \prime }-2 a y^{\prime }+a^{2} y&={\mathrm e}^{a x}+f^{\prime \prime }\left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| 12770 |
\begin{align*}
2 y^{\prime \prime } x +\left (-x +2\right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.087 |
|
| 12771 |
\begin{align*}
4 x \left (x -1\right ) \left (x -2\right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.087 |
|
| 12772 |
\begin{align*}
x {y^{\prime }}^{2}+x y y^{\prime \prime }&=3 y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.088 |
|
| 12773 |
\begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.088 |
|
| 12774 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.088 |
|
| 12775 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.088 |
|
| 12776 |
\begin{align*}
a y+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| 12777 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-x_{2}-2 x_{3}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}+3 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| 12778 |
\begin{align*}
x^{\prime }-x+y&=\sec \left (t \right ) \\
-2 x+y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| 12779 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{3}+24 t \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
x_{3}^{\prime }&=3 x_{1}-x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| 12780 |
\begin{align*}
3 x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| 12781 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {n \left (n +1\right ) y}{x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| 12782 |
\begin{align*}
3 y+2 \cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.090 |
|
| 12783 |
\begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.090 |
|
| 12784 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.090 |
|
| 12785 |
\begin{align*}
t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&={\mathrm e}^{-t} t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.090 |
|
| 12786 |
\begin{align*}
y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=f \left (t \right ) \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.090 |
|
| 12787 |
\begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+16 \left (2+x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.091 |
|
| 12788 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -2 y&=x^{2}-2 x +2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.091 |
|
| 12789 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+y p&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.091 |
|
| 12790 |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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✓ |
✓ |
✓ |
1.091 |
|
| 12791 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+5 x&=\delta \left (t -\pi \right )+\delta \left (t -2 \pi \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
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✓ |
✓ |
✓ |
1.092 |
|
| 12792 |
\begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
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✓ |
✓ |
✓ |
1.092 |
|
| 12793 |
\begin{align*}
x^{\prime }&=x-12 y-14 z \\
y^{\prime }&=x+2 y-3 z \\
z^{\prime }&=x+y-2 z \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 6 \\
z \left (0\right ) &= -7 \\
\end{align*} |
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✓ |
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✓ |
1.092 |
|
| 12794 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=x \\
\end{align*} |
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✓ |
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✓ |
1.092 |
|
| 12795 |
\begin{align*}
y^{\prime \prime }+16 y&=\csc \left (4 t \right ) \\
\end{align*} |
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1.092 |
|
| 12796 |
\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 \(x=0\). |
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1.092 |
|
| 12797 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2}+\csc \left (t \right ) \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+\sec \left (t \right ) \\
\end{align*} |
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✓ |
1.093 |
|
| 12798 |
\begin{align*}
y^{\prime }&=x -\frac {1}{3} x^{3} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
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1.093 |
|
| 12799 |
\begin{align*}
\left (x^{2}-3 x -4\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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1.093 |
|
| 12800 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
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✓ |
1.093 |
|