| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12701 |
\begin{align*}
y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta f \left (x \right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.112 |
|
| 12702 |
\begin{align*}
x y^{\prime \prime }&=-y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| 12703 |
\begin{align*}
e y^{\prime \prime }&=-P \left (L -x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| 12704 |
\begin{align*}
x^{\prime \prime }+x&=\sin \left (2 t \right )-\cos \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| 12705 |
\begin{align*}
y_{1}^{\prime }&=y_{2}+y_{3}+{\mathrm e}^{2 t} \\
y_{2}^{\prime }&=y_{1}+y_{2}-y_{3}+{\mathrm e}^{2 t} \\
y_{3}^{\prime }&=-2 y_{1}+y_{2}+3 y_{3}-{\mathrm e}^{2 t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 0 \\
y_{3} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| 12706 |
\begin{align*}
\left (x -2\right )^{2} y^{\prime \prime }+3 \left (x -2\right ) y^{\prime }-3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.112 |
|
| 12707 |
\begin{align*}
2 \sin \left (t \right ) y^{\prime \prime }+\left (1-t \right ) y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
1.113 |
|
| 12708 |
\begin{align*}
\sin \left (x \right )^{2} y^{\prime \prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.113 |
|
| 12709 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.113 |
|
| 12710 |
\begin{align*}
y^{\prime }-5 y&=2 \,{\mathrm e}^{-t}+\delta \left (-3+t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.114 |
|
| 12711 |
\begin{align*}
2 x^{\prime }+y^{\prime }+x+y&=t^{2}+4 t \\
x^{\prime }+y^{\prime }+2 x+2 y&=2 t^{2}-2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.114 |
|
| 12712 |
\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*} |
✓ |
✓ |
✓ |
✓ |
1.115 |
|
| 12713 |
\begin{align*}
{\mathrm e}^{x} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+2 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.115 |
|
| 12714 |
\begin{align*}
2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.115 |
|
| 12715 |
\begin{align*}
x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x&=\cos \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.115 |
|
| 12716 |
\begin{align*}
\cos \left (x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.115 |
|
| 12717 |
\begin{align*}
x^{\prime }&=-y+z \\
y^{\prime }&=z \\
z^{\prime }&=-x+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.115 |
|
| 12718 |
\begin{align*}
y^{\prime \prime }+16 y&=5 \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.115 |
|
| 12719 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{2 x}}{\left (1+{\mathrm e}^{x}\right )^{2}} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= {\frac {5}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.115 |
|
| 12720 |
\begin{align*}
-2 y^{\prime }+x y^{\prime \prime }&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.115 |
|
| 12721 |
\begin{align*}
y^{\prime \prime }+9 y&=9 \sec \left (3 t \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| 12722 |
\begin{align*}
y^{\prime \prime }+t y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.116 |
|
| 12723 |
\begin{align*}
t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| 12724 |
\begin{align*}
-2 y+y^{\prime }&=\delta \left (t -2\right ) \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| 12725 |
\begin{align*}
x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.116 |
|
| 12726 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| 12727 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| 12728 |
\begin{align*}
-y^{\prime }+x y^{\prime \prime }&=6 x^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| 12729 |
\begin{align*}
-y^{\prime }+x y^{\prime \prime }&=3 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| 12730 |
\begin{align*}
y^{\prime \prime }&=x^{2} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| 12731 |
\begin{align*}
2 x \left (x +1\right ) y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| 12732 |
\begin{align*}
y&=x y^{\prime }+\frac {a}{{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.116 |
|
| 12733 |
\begin{align*}
16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| 12734 |
\begin{align*}
y^{\prime \prime }-8 y^{\prime }+17 y&={\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| 12735 |
\begin{align*}
\left (\left (1-a \right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+x^{2}+\left (1-a \right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.117 |
|
| 12736 |
\begin{align*}
4 y+y^{\prime \prime }&=8 \sin \left (2 x \right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| 12737 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| 12738 |
\begin{align*}
y^{\prime }&=\frac {y^{2}+5}{y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| 12739 |
\begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{-x^{2}} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| 12740 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| 12741 |
\begin{align*}
x y^{n}+2 y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.118 |
|
| 12742 |
\begin{align*}
a x y^{\prime }+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.118 |
|
| 12743 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| 12744 |
\begin{align*}
x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.118 |
|
| 12745 |
\begin{align*}
y^{\prime \prime }&=2 a \left (c +b x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.118 |
|
| 12746 |
\begin{align*}
2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=10 x +\frac {10}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| 12747 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \arcsin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| 12748 |
\begin{align*}
y^{\prime \prime }-9 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| 12749 |
\begin{align*}
y^{\prime \prime }+4 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| 12750 |
\begin{align*}
x \ln \left (x \right ) y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| 12751 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+x^{3} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| 12752 |
\begin{align*}
\left (x^{2}+x \right ) y^{\prime }+2 x +1+2 \cos \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| 12753 |
\begin{align*}
2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.118 |
|
| 12754 |
\begin{align*}
y^{\prime \prime }-y^{\prime }&={\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| 12755 |
\begin{align*}
2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.119 |
|
| 12756 |
\begin{align*}
2 x y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.119 |
|
| 12757 |
\begin{align*}
2 y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.119 |
|
| 12758 |
\begin{align*}
t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
1.120 |
|
| 12759 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+x&=-6+2 \,{\mathrm e}^{2 t} \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.120 |
|
| 12760 |
\begin{align*}
y^{\prime }&=\frac {x}{2}-y+\frac {3}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.120 |
|
| 12761 |
\begin{align*}
\left (4 x +3\right ) y+16 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.121 |
|
| 12762 |
\begin{align*}
3 x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}+2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.121 |
|
| 12763 |
\begin{align*}
y^{\prime \prime }+y&=\frac {1}{\cos \left (2 x \right )^{{3}/{2}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.121 |
|
| 12764 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }-12 y&=\delta \left (-3+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.122 |
|
| 12765 |
\begin{align*}
x \left (1-x \right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+10 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.122 |
|
| 12766 |
\begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }-10 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.122 |
|
| 12767 |
\begin{align*}
x^{\prime }+3 y^{\prime }+y&={\mathrm e}^{t} \\
-x+y^{\prime }&=y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.122 |
|
| 12768 |
\begin{align*}
y^{\prime } \left (2 y-y^{\prime }\right )&=y^{2} \sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.122 |
|
| 12769 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{x} \left (x +1\right )+2 \,{\mathrm e}^{2 x}+3 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.123 |
|
| 12770 |
\begin{align*}
y^{\prime }+\frac {n y}{x}&=a \,x^{-n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.123 |
|
| 12771 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3}+2 \,{\mathrm e}^{8 t} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{3}+{\mathrm e}^{8 t} \\
x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3}+2 \,{\mathrm e}^{8 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.124 |
|
| 12772 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a +2 b \right ) x^{2} y^{\prime }+\left (\left (a +b \right ) b \,x^{2}-2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.124 |
|
| 12773 |
\begin{align*}
\left (-x^{2}+2\right ) y+4 x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.124 |
|
| 12774 |
\begin{align*}
x^{\prime }&=2 x+2 y \\
y^{\prime }&=6 x+3 y+{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.124 |
|
| 12775 |
\begin{align*}
x^{\prime }-x-y&=0 \\
5 x+y^{\prime }-3 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.124 |
|
| 12776 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}+{\mathrm e}^{3 t} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2}+{\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.125 |
|
| 12777 |
\begin{align*}
\operatorname {A4} y+\operatorname {A3} x y^{\prime }+\operatorname {A2} \,x^{2} y^{\prime \prime }+\operatorname {A1} \,x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.125 |
|
| 12778 |
\begin{align*}
y^{\prime \prime }-y^{\prime }+4 y&=x \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.125 |
|
| 12779 |
\begin{align*}
\left (x y^{\prime }+a \right )^{2}-2 a y+x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.125 |
|
| 12780 |
\begin{align*}
y^{\prime }&=\frac {-2 x -y+F \left (x \left (x +y\right )\right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.125 |
|
| 12781 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=x \,{\mathrm e}^{x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.125 |
|
| 12782 |
\begin{align*}
y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y&=-3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.125 |
|
| 12783 |
\begin{align*}
x^{\prime \prime }-\frac {x^{\prime } t}{4}+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.125 |
|
| 12784 |
\begin{align*}
x^{2} \left (1+4 x \right ) y^{\prime \prime }-x \left (1-4 x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.126 |
|
| 12785 |
\begin{align*}
y^{\prime \prime }+4 y&=\delta \left (t -\pi \right ) \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.126 |
|
| 12786 |
\begin{align*}
y^{\prime \prime }+12 y^{\prime }+37 y&={\mathrm e}^{-6 t} \csc \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.126 |
|
| 12787 |
\begin{align*}
\left (t^{2}+t \right ) y^{\prime \prime \prime }+\left (-t^{2}+2\right ) y^{\prime \prime }-\left (t +2\right ) y^{\prime }&=-2-t \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.126 |
|
| 12788 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=g \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.126 |
|
| 12789 |
\begin{align*}
{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.127 |
|
| 12790 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 x}}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.127 |
|
| 12791 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2+{\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.127 |
|
| 12792 |
\begin{align*}
t^{2} y^{\prime \prime }+t^{2} y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.127 |
|
| 12793 |
\begin{align*}
x y^{\prime }+\left (2 x -3\right ) y&=4 x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.128 |
|
| 12794 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}+5 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-6 x_{1}-6 x_{2}-5 x_{3} \\
x_{3}^{\prime }&=6 x_{1}+6 x_{2}+5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.128 |
|
| 12795 |
\begin{align*}
y \sin \left (x \right )-2 \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime }&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.128 |
|
| 12796 |
\begin{align*}
y^{\prime }+y \tan \left (x \right )&=y^{3} \sec \left (x \right )^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.128 |
|
| 12797 |
\begin{align*}
y^{\prime }+2 x y^{\prime \prime }&=\sqrt {x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.128 |
|
| 12798 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.128 |
|
| 12799 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-3 x_{2}+34 \sin \left (t \right ) \\
x_{2}^{\prime }&=-4 x_{1}-2 x_{2}+17 \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.129 |
|
| 12800 |
\begin{align*}
2 y^{3} y^{\prime }+x y^{2}-x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.129 |
|