| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 4001 |
\begin{align*}
y^{\prime }&=3 x +\frac {y}{x} \\
y \left (1\right ) &= 3 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| 4002 |
\begin{align*}
\left (-x^{2}+1\right ) {y^{\prime }}^{2}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| 4003 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+5 y&=29 \cos \left (2 t \right ) \\
y \left (0\right ) &= {\frac {16}{5}} \\
y^{\prime }\left (0\right ) &= {\frac {31}{5}} \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| 4004 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.312 |
|
| 4005 |
\begin{align*}
y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime }&=3 \,{\mathrm e}^{-x}+6 \,{\mathrm e}^{2 x}-6 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| 4006 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| 4007 |
\begin{align*}
x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+17 y^{\prime } x -17 y&=0 \\
y \left (1\right ) &= -2 \\
y^{\prime }\left (1\right ) &= 0 \\
y^{\prime \prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| 4008 |
\begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| 4009 |
\begin{align*}
y_{1}^{\prime }&=2 y_{1}-64 y_{2} \\
y_{2}^{\prime }&=y_{1}-14 y_{2} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| 4010 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| 4011 |
\begin{align*}
\sin \left (\theta \right )^{2} r^{\prime }&=-b \cos \left (\theta \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| 4012 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| 4013 |
\begin{align*}
y^{\prime }&=2 x +1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| 4014 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2} \\
x_{2}^{\prime }&=6 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| 4015 |
\begin{align*}
x_{1}^{\prime }&=6 x_{1}-7 x_{2} \\
x_{2}^{\prime }&=x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| 4016 |
\begin{align*}
y^{3}-x y^{2}+2 x^{2} y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| 4017 |
\begin{align*}
2 y \,{\mathrm e}^{2 x}+2 x \cos \left (y\right )+\left ({\mathrm e}^{2 x}-x^{2} \sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.313 |
|
| 4018 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| 4019 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x +28 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.313 |
|
| 4020 |
\begin{align*}
x^{\prime }&=a x-y \\
y^{\prime }&=x+a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| 4021 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| 4022 |
\begin{align*}
x y^{\prime \prime \prime }+2 y^{\prime \prime }&=6 x \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
y^{\prime \prime }\left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| 4023 |
\begin{align*}
y^{\prime }&=x \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| 4024 |
\begin{align*}
x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+5 y^{\prime } x -5 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= -1 \\
y^{\prime \prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| 4025 |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| 4026 |
\begin{align*}
y^{\prime \prime }+4 y&=3 \,{\mathrm e}^{-2 t} \sin \left (2 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| 4027 |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| 4028 |
\begin{align*}
y^{\prime }&=\frac {1}{\sqrt {-x^{2}+1}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| 4029 |
\begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| 4030 |
\begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.314 |
|
| 4031 |
\begin{align*}
x^{\prime }-x-2 y&=16 \,{\mathrm e}^{t} t \\
2 x-y^{\prime }-2 y&=0 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.314 |
|
| 4032 |
\begin{align*}
x^{2} {y^{\prime }}^{2}&=a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.314 |
|
| 4033 |
\begin{align*}
y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.314 |
|
| 4034 |
\begin{align*}
y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.314 |
|
| 4035 |
\begin{align*}
x^{\prime }&=3 t^{2}+4 t \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.314 |
|
| 4036 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.314 |
|
| 4037 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x&={\mathrm e}^{-x} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.314 |
|
| 4038 |
\begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.314 |
|
| 4039 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x -2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| 4040 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+13 x&=t \,{\mathrm e}^{-t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| 4041 |
\begin{align*}
y_{1}^{\prime }&=-\frac {4 y_{1}}{5}+\frac {3 y_{2}}{5} \\
y_{2}^{\prime }&=-\frac {2 y_{1}}{5}-\frac {11 y_{2}}{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| 4042 |
\begin{align*}
2 y y^{\prime \prime }&=4 y^{2} \left (x +2 y\right )+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.315 |
|
| 4043 |
\begin{align*}
u^{\prime }+b u^{2}&=\frac {c}{x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| 4044 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.315 |
|
| 4045 |
\begin{align*}
x^{\prime }&=12 x+18 y \\
y^{\prime }&=-8 x-12 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| 4046 |
\begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| 4047 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=30 x \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| 4048 |
\begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-5 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| 4049 |
\begin{align*}
y_{1}^{\prime }&=-4 y_{1}-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 ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| 4050 |
\begin{align*}
y^{\prime \prime \prime } \csc \left (x \right )^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| 4051 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime } x +y&=4 x y^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.315 |
|
| 4052 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| 4053 |
\begin{align*}
x \left (1-2 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+4 x^{2} \ln \left (x \right )\right ) y^{\prime }-\left (2+4 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.315 |
|
| 4054 |
\begin{align*}
y^{\prime }&=3 y \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| 4055 |
\begin{align*}
y^{\prime }&=\frac {10}{x^{2}+1} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| 4056 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| 4057 |
\begin{align*}
t \left (-2+t \right )^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*} Series expansion around \(t=2\). |
✗ |
✗ |
✓ |
✗ |
0.316 |
|
| 4058 |
\begin{align*}
y^{\prime }+4 y&=1 \\
y \left (0\right ) &= {\frac {5}{4}} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| 4059 |
\begin{align*}
4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (4 x +1\right ) y^{\prime }-\left (49+27 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.316 |
|
| 4060 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.316 |
|
| 4061 |
\begin{align*}
a x +y {y^{\prime }}^{2}+y^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.316 |
|
| 4062 |
\begin{align*}
y^{\prime }&=x -\frac {1}{3} x^{3} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| 4063 |
\begin{align*}
x^{\prime }&=-3 x-y \\
y^{\prime }&=x-5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| 4064 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{2}+1} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| 4065 |
\begin{align*}
y_{1}^{\prime }&=5 y_{1}-2 y_{2} \\
y_{2}^{\prime }&=6 y_{1}-2 y_{2} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| 4066 |
\begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| 4067 |
\begin{align*}
x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| 4068 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.317 |
|
| 4069 |
\begin{align*}
y+x \left (x^{2} y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.317 |
|
| 4070 |
\begin{align*}
\sqrt {x +4}\, y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.317 |
|
| 4071 |
\begin{align*}
y^{\prime \prime }+w^{2} y&=\cos \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.317 |
|
| 4072 |
\begin{align*}
\left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.317 |
|
| 4073 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.318 |
|
| 4074 |
\begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2} \\
y_{2}^{\prime }&=3 y_{2}-y_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.318 |
|
| 4075 |
\begin{align*}
y^{\prime } x +\sqrt {x}&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.318 |
|
| 4076 |
\begin{align*}
y^{\prime }&=\arcsin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.318 |
|
| 4077 |
\begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.318 |
|
| 4078 |
\begin{align*}
y^{\prime \prime }-\left (x -1\right ) y^{\prime }&=x^{2}-2 x \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✗ |
0.318 |
|
| 4079 |
\begin{align*}
-t y^{\prime \prime }-2 y^{\prime }+t y&=0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.318 |
|
| 4080 |
\begin{align*}
y^{\prime \prime }+y&=x \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.319 |
|
| 4081 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=6 x_{1}-5 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 4082 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +2 \alpha y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 4083 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 4084 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=8 \sin \left (t \right ) {\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 4085 |
\begin{align*}
x^{\prime }-4 x+3 y&=\sin \left (t \right ) \\
2 x+y^{\prime }-y&=2 \cos \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= x_{0} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 4086 |
\begin{align*}
z^{\prime }-x^{2} z&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 4087 |
\begin{align*}
x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.319 |
|
| 4088 |
\begin{align*}
x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.319 |
|
| 4089 |
\(\left [\begin {array}{ccc} 1 & 0 & 0 \\ -4 & 7 & 2 \\ 10 & -15 & -4 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.319 |
|
| 4090 |
\begin{align*}
\left (2 x^{2}-3\right ) y^{\prime \prime }-2 y^{\prime } x +y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 4091 |
\begin{align*}
y^{\prime }&=\sin \left (\frac {x}{2}\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 4092 |
\begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}+5 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.319 |
|
| 4093 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (x +4\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.319 |
|
| 4094 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=8 x_{1}-4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| 4095 |
\begin{align*}
2 y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| 4096 |
\begin{align*}
2 y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.320 |
|
| 4097 |
\begin{align*}
y^{\prime \prime }-2 y x&=0 \\
y \left (2\right ) &= 1 \\
y^{\prime }\left (2\right ) &= 6 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| 4098 |
\begin{align*}
y^{\prime \prime }-y x&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| 4099 |
\begin{align*}
x^{\prime \prime \prime \prime }-x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
x^{\prime \prime }\left (0\right ) &= 0 \\
x^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.321 |
|
| 4100 |
\begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.321 |
|