| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 9001 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=3 \cos \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| 9002 |
\begin{align*}
y^{\prime }-\tan \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| 9003 |
\begin{align*}
y^{\prime \prime }+4 y&=\sin \left (t \right )-\sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| 9004 |
\begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| 9005 |
\begin{align*}
y^{\prime \prime }-y&=\frac {2 \,{\mathrm e}^{-x}}{\left (1+{\mathrm e}^{-2 x}\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| 9006 |
\begin{align*}
y^{\prime }&=1+3 \tan \left (x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| 9007 |
\begin{align*}
y^{\prime \prime }&=\operatorname {a0} +\operatorname {a2} y+\operatorname {a1} x y+\operatorname {a3} y^{3} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.593 |
|
| 9008 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 x} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| 9009 |
\begin{align*}
\left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| 9010 |
\begin{align*}
y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=-2\). |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| 9011 |
\begin{align*}
t y^{\prime \prime }-y^{\prime } t +y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.593 |
|
| 9012 |
\begin{align*}
6 x^{2} y^{\prime \prime }+\left (x^{3}+11 x \right ) y^{\prime }+\left (-2 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| 9013 |
\begin{align*}
y^{\prime \prime } x +x^{2} y^{\prime }+\left ({\mathrm e}^{x}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| 9014 |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (1+t \right )}+y&=0 \\
\end{align*} Series expansion around \(t=-1\). |
✗ |
✗ |
✓ |
✗ |
0.594 |
|
| 9015 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{t}+{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| 9016 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+\left (1+\lambda \right ) y&=0 \\
y \left (0\right ) &= 0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| 9017 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=6 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| 9018 |
\begin{align*}
2 y+y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| 9019 |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| 9020 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=1+\sin \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.594 |
|
| 9021 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.594 |
|
| 9022 |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}+x^{2} y y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.594 |
|
| 9023 |
\begin{align*}
y^{\prime }&=\frac {-2 x -10}{\left (2+x \right ) \left (x -4\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| 9024 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| 9025 |
\begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2} \\
y_{2}^{\prime }&=y_{1}-y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| 9026 |
\begin{align*}
4 y+y^{\prime \prime }&=8 \sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| 9027 |
\begin{align*}
-\left (-2 x^{2}+3\right ) y+4 x^{3} y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.595 |
|
| 9028 |
\begin{align*}
2 y^{\prime \prime } x +5 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| 9029 |
\begin{align*}
-8 y+2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| 9030 |
\begin{align*}
x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.595 |
|
| 9031 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=4 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| 9032 |
\begin{align*}
x^{\prime \prime }+x&=\sin \left (t \right )-\cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| 9033 |
\begin{align*}
\left (1-y\right ) y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.595 |
|
| 9034 |
\begin{align*}
y&=x {y^{\prime }}^{2}+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| 9035 |
\begin{align*}
y^{\prime }&=40 x \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| 9036 |
\begin{align*}
\left (x^{2}+4\right )^{2} y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| 9037 |
\begin{align*}
x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+7 y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| 9038 |
\begin{align*}
r^{\prime \prime }+r^{\prime }+r&=1 \\
r \left (0\right ) &= 0 \\
r^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| 9039 |
\begin{align*}
x^{\prime \prime }+4 x&=\delta \left (t \right )+\delta \left (t -\pi \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| 9040 |
\begin{align*}
t^{2} y^{\prime \prime }-2 y&=3 t^{2}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| 9041 |
\begin{align*}
\left (x^{2}-2 x -3\right ) y^{\prime \prime }+y^{\prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=4\). |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| 9042 |
\begin{align*}
y^{\prime \prime }+y&=t^{2} \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| 9043 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{49}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| 9044 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{2}+x +1 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.596 |
|
| 9045 |
\begin{align*}
y^{\prime }&=f \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| 9046 |
\begin{align*}
y^{\prime \prime \prime }+4 y^{\prime }&=\sec \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| 9047 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-8 y&=-t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| 9048 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=2 \sinh \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.596 |
|
| 9049 |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| 9050 |
\begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| 9051 |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=-b x_{1}-a x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.597 |
|
| 9052 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.597 |
|
| 9053 |
\begin{align*}
\left (-x^{2}+1\right ) y-x \left (-x^{2}+1\right ) y^{\prime }+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.597 |
|
| 9054 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=-50 \sin \left (5 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.597 |
|
| 9055 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.597 |
|
| 9056 |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }-8 y&={\mathrm e}^{x} \left (x^{2}+2\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.597 |
|
| 9057 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.597 |
|
| 9058 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.598 |
|
| 9059 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+5 x&=10 \cos \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| 9060 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| 9061 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| 9062 |
\begin{align*}
a^{2} y+\left (x^{2}+y^{2}\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.598 |
|
| 9063 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| 9064 |
\begin{align*}
y^{\prime }&=\ln \left (x \right ) \\
y \left ({\mathrm e}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| 9065 |
\begin{align*}
\left (-4 x^{2}+1\right ) y^{\prime \prime }+8 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| 9066 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| 9067 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\cos \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| 9068 |
\begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2} \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 15 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.598 |
|
| 9069 |
\begin{align*}
y^{\prime }&=\left (-1+y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| 9070 |
\begin{align*}
x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.598 |
|
| 9071 |
\begin{align*}
y^{\prime \prime } x -\left (x +4\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.598 |
|
| 9072 |
\begin{align*}
y^{\prime \prime }+\left (x -1\right )^{2} y^{\prime }-4 \left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| 9073 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-9 x+6 y+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| 9074 |
\begin{align*}
y^{\prime \prime }+y&=x +{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| 9075 |
\begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right ) \csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| 9076 |
\begin{align*}
y^{\prime }&=2-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| 9077 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-3 x_{2} \\
x_{2}^{\prime }&=-2 x_{1}+2 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| 9078 |
\begin{align*}
y^{\prime \prime }-y&=\frac {1}{\sqrt {1-{\mathrm e}^{2 x}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| 9079 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| 9080 |
\begin{align*}
\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| 9081 |
\begin{align*}
a y \left (-1+y\right ) y^{\prime \prime }-\left (-1+a \right ) \left (-1+2 y\right ) {y^{\prime }}^{2}+f y \left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.599 |
|
| 9082 |
\begin{align*}
y^{\prime \prime }-4 y&=32 t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| 9083 |
\begin{align*}
y^{\prime \prime }-4 x^{2} y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| 9084 |
\begin{align*}
4 x^{\prime \prime }+2 x^{\prime }+8 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| 9085 |
\begin{align*}
x^{2} y^{\prime \prime }&=\left (3 x -2 y^{\prime }\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| 9086 |
\begin{align*}
t^{2} x^{\prime \prime }-3 t x^{\prime }+\left (4-t \right ) x&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.599 |
|
| 9087 |
\begin{align*}
y^{\prime \prime }+3 y&=-x^{6}+x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| 9088 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&=\frac {6}{1+{\mathrm e}^{-2 x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.599 |
|
| 9089 |
\begin{align*}
y^{\prime }&=1+y \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| 9090 |
\begin{align*}
2 \left (b x +3 a \right ) y-2 x \left (b x +2 a \right ) y^{\prime }+x^{2} \left (b x +a \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.600 |
|
| 9091 |
\begin{align*}
2 y y^{\prime \prime }&=f \left (x \right ) y^{2}+3 {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.600 |
|
| 9092 |
\begin{align*}
y^{\prime }-{\mathrm e}^{x} y&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.600 |
|
| 9093 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+4 y x&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.600 |
|
| 9094 |
\begin{align*}
-y+y^{\prime }&=2 \cos \left (5 t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.600 |
|
| 9095 |
\begin{align*}
\frac {x^{\prime \prime }}{2}+\frac {5 x^{\prime }}{6}+\frac {2 x}{9}&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.600 |
|
| 9096 |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }&=\left (x -1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.600 |
|
| 9097 |
\begin{align*}
y&=y^{\prime } x -\sqrt {y^{\prime }-1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.600 |
|
| 9098 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x}+7 x -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.600 |
|
| 9099 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (3 x^{4}+5 x \right ) y^{\prime }+\left (6 x^{3}+5\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.600 |
|
| 9100 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}-6 x_{3} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}-2 x_{3} \\
x_{3}^{\prime }&=4 x_{1}-2 x_{2}-4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.601 |
|