| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 8101 |
\begin{align*}
y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y&=20 \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.031 |
|
| 8102 |
\begin{align*}
y^{\prime \prime }&=x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| 8103 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| 8104 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| 8105 |
\begin{align*}
{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| 8106 |
\begin{align*}
4 y+4 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
y^{\prime \prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| 8107 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=\sin \left (t \right )+{\mathrm e}^{2 t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 8108 |
\begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 8109 |
\begin{align*}
x^{\prime }+y^{\prime }&=y \\
x^{\prime }-y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 8110 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=-3 \,{\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 8111 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 8112 |
\begin{align*}
x^{\prime }-7 x+y&=0 \\
y^{\prime }-2 x-5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 8113 |
\begin{align*}
y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| 8114 |
\begin{align*}
x^{2} \left (x +4\right ) y^{\prime \prime }+x \left (-1+x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.034 |
|
| 8115 |
\begin{align*}
y^{\prime }&=\frac {t^{2}+1}{t \left (-2+t \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.034 |
|
| 8116 |
\begin{align*}
t^{2} y^{\prime \prime }-5 y^{\prime } t +9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.035 |
|
| 8117 |
\begin{align*}
y y^{\prime \prime }&=y^{2} \left (f \left (x \right ) y+g^{\prime }\left (x \right )\right )+y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.035 |
|
| 8118 |
\begin{align*}
f \left (x \right )+a y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.035 |
|
| 8119 |
\begin{align*}
2 \,{\mathrm e}^{2 x} y+2 x \cos \left (y\right )+\left ({\mathrm e}^{2 x}-x^{2} \sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.035 |
|
| 8120 |
\begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=-3 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.035 |
|
| 8121 |
\begin{align*}
y {y^{\prime }}^{2}-\left (y x +x +y^{2}\right ) y^{\prime }+x^{2}+y x&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.035 |
|
| 8122 |
\begin{align*}
y^{\prime \prime } x +y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| 8123 |
\begin{align*}
x^{\prime }&=y+\textit {f\_1} \left (t \right ) \\
y^{\prime }&=-x+f_{2} \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| 8124 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| 8125 |
\begin{align*}
x^{\prime }&=3 x-y+1 \\
y^{\prime }&=x+y+2 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| 8126 |
\begin{align*}
x^{\prime \prime }+\frac {x^{\prime }}{10}+x&=3 \cos \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| 8127 |
\begin{align*}
v^{\prime \prime }+\frac {2 v^{\prime }}{r}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| 8128 |
\begin{align*}
x^{\prime \prime }-4 x^{\prime }+13 x&=20 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| 8129 |
\begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| 8130 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y \ln \left (x \right )&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.037 |
|
| 8131 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+4 y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.037 |
|
| 8132 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x^{2}+x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.037 |
|
| 8133 |
\begin{align*}
4 y^{\prime \prime }+5 y^{\prime }+4 y&=3 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.037 |
|
| 8134 |
\begin{align*}
y^{\prime \prime }+16 y^{\prime }&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.037 |
|
| 8135 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=6 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.037 |
|
| 8136 |
\begin{align*}
9 y^{\prime \prime }-6 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.037 |
|
| 8137 |
\begin{align*}
x^{3} \left (-x^{2}+1\right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
1.037 |
|
| 8138 |
\begin{align*}
t^{2} y^{\prime \prime }-2 y&=3 t^{2}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.038 |
|
| 8139 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2}+3 x_{3} \\
x_{2}^{\prime }&=-9 x_{1}-3 x_{2}-9 x_{3} \\
x_{3}^{\prime }&=4 x_{1}+4 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.038 |
|
| 8140 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.038 |
|
| 8141 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-x^{2}-6 x +1\right ) y^{\prime }+\left (x^{2}+6 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| 8142 |
\begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| 8143 |
\begin{align*}
4 x^{2} \left (x +1\right ) y^{\prime \prime }-5 y^{\prime } x +2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| 8144 |
\begin{align*}
-\left (-4 x^{2}+4 x +1\right ) y+4 x \left (1-2 x \right ) y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.039 |
|
| 8145 |
\begin{align*}
y^{\prime \prime }-y&=\sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| 8146 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| 8147 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
y^{\prime \prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| 8148 |
\begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=x^{2} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| 8149 |
\begin{align*}
x^{\prime }-x-2 y&=0 \\
y^{\prime }-2 y-3 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| 8150 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\
y \left (2\right ) &= 10 \\
y^{\prime }\left (2\right ) &= 15 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| 8151 |
\begin{align*}
6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| 8152 |
\begin{align*}
2 {y^{\prime }}^{3}-3 {y^{\prime }}^{2}+x&=y \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.040 |
|
| 8153 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+k y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| 8154 |
\begin{align*}
b y+a y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.040 |
|
| 8155 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{-2 t} \\
x_{2}^{\prime }&=4 x_{1}-2 x_{2}-2 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| 8156 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime }&=3 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{-x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
y^{\prime \prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
1.040 |
|
| 8157 |
\begin{align*}
z^{\prime \prime }+8 z^{\prime }+16 z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| 8158 |
\begin{align*}
a \,x^{2} y y^{\prime \prime }+b \,x^{2} {y^{\prime }}^{2}+c x y y^{\prime }+d y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.041 |
|
| 8159 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.041 |
|
| 8160 |
\begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=3 x +4 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
y^{\prime \prime \prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.041 |
|
| 8161 |
\begin{align*}
y^{\prime \prime }+y&=3 \cos \left (w t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.041 |
|
| 8162 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.042 |
|
| 8163 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+8 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.042 |
|
| 8164 |
\begin{align*}
y^{\prime }&=\frac {1}{-1+x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.042 |
|
| 8165 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2} \\
x_{2}^{\prime }&=-14 x_{1}-5 x_{2}+x_{3} \\
x_{3}^{\prime }&=15 x_{1}+5 x_{2}-2 x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 5 \\
x_{2} \left (0\right ) &= 5 \\
x_{3} \left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.042 |
|
| 8166 |
\begin{align*}
y^{\prime \prime }+y&=x \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.042 |
|
| 8167 |
\begin{align*}
4 y^{\prime \prime }+8 y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.042 |
|
| 8168 |
\begin{align*}
2 y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| 8169 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=4 \sinh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.043 |
|
| 8170 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=5 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| 8171 |
\begin{align*}
x V^{\prime }&=x^{2}+1 \\
V \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| 8172 |
\begin{align*}
2 z^{\prime \prime }+7 z^{\prime }-4 z&=0 \\
z \left (0\right ) &= 0 \\
z^{\prime }\left (0\right ) &= 9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| 8173 |
\begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| 8174 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| 8175 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| 8176 |
\begin{align*}
-4 y^{\prime }+y^{\prime \prime \prime }&=x^{2}-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| 8177 |
\begin{align*}
4 f \left (x \right ) y y^{\prime \prime }&=4 f \left (x \right )^{2} y+3 f \left (x \right ) g \left (x \right ) y^{2}-f \left (x \right ) y^{4}+2 y^{3} f^{\prime }\left (x \right )+\left (-6 f \left (x \right ) y^{2}+2 f^{\prime }\left (x \right )\right ) y^{\prime }+3 f \left (x \right ) {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.044 |
|
| 8178 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+8 y&=8 \,{\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.044 |
|
| 8179 |
\begin{align*}
4 x^{2} y^{\prime \prime }+y&=8 \sqrt {x}\, \left (1+\ln \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.044 |
|
| 8180 |
\begin{align*}
\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.044 |
|
| 8181 |
\begin{align*}
x^{\prime }&=1 \\
y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.044 |
|
| 8182 |
\begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=4 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.044 |
|
| 8183 |
\begin{align*}
2 t^{2} y^{\prime \prime }+3 y^{\prime } t -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.045 |
|
| 8184 |
\begin{align*}
3 {y^{\prime }}^{5}-y y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.045 |
|
| 8185 |
\begin{align*}
a y^{2}+x^{3} y^{\prime } y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
1.045 |
|
| 8186 |
\begin{align*}
y^{\left (5\right )}-y^{\prime \prime \prime \prime }-y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.045 |
|
| 8187 |
\begin{align*}
y^{\prime \prime }+\sin \left (x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.045 |
|
| 8188 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (\pi \right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.045 |
|
| 8189 |
\begin{align*}
3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| 8190 |
\begin{align*}
y^{\prime \prime }+y&=x^{3}+x^{2}+x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| 8191 |
\begin{align*}
1&=\left (x^{2}-9\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| 8192 |
\begin{align*}
y^{\prime \prime }+4 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| 8193 |
\begin{align*}
y^{\prime \prime }+\frac {3 y^{\prime }}{x}+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| 8194 |
\begin{align*}
y^{\prime \prime \prime }+7 y^{\prime \prime }+19 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
y^{\prime \prime }\left (0\right ) &= -12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| 8195 |
\begin{align*}
x_{1}^{\prime }&=-x_{2} \\
x_{2}^{\prime }&=x_{1} \\
x_{3}^{\prime }&=x_{2}-x_{4} \\
x_{4}^{\prime }&=x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.047 |
|
| 8196 |
\begin{align*}
-y+2 n y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.047 |
|
| 8197 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.047 |
|
| 8198 |
\begin{align*}
y y^{\prime \prime }&=g \left (x \right ) y^{2}+f \left (x \right ) y y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.047 |
|
| 8199 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (1\right ) &= {\mathrm e}^{2} \\
y^{\prime }\left (1\right ) &= 3 \,{\mathrm e}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.047 |
|
| 8200 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=3-4 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.047 |
|