| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 8901 |
\begin{align*}
x^{2} \left (2+x \right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| 8902 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}+6 x \right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| 8903 |
\begin{align*}
9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.902 |
|
| 8904 |
\begin{align*}
4 x^{\prime }-y^{\prime }+3 x&=\sin \left (t \right ) \\
x^{\prime }+y&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| 8905 |
\begin{align*}
x^{\prime }&=\frac {-x+x^{2}}{2 x-1} \\
x \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| 8906 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.903 |
|
| 8907 |
\begin{align*}
\left ({\mathrm e}^{t}-1\right ) y^{\prime \prime }+{\mathrm e}^{t} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.903 |
|
| 8908 |
\begin{align*}
2 x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.903 |
|
| 8909 |
\begin{align*}
2 y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.903 |
|
| 8910 |
\begin{align*}
y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.903 |
|
| 8911 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime } x +\left (2 x^{2}+5\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.903 |
|
| 8912 |
\begin{align*}
y^{\prime \prime }-{\mathrm e}^{x} y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.903 |
|
| 8913 |
\begin{align*}
y^{\prime \prime }+y&=2 \sin \left (2 x \right ) \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.903 |
|
| 8914 |
\begin{align*}
x^{2}+y+y^{2}-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.903 |
|
| 8915 |
\begin{align*}
1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.904 |
|
| 8916 |
\begin{align*}
12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.904 |
|
| 8917 |
\begin{align*}
\sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 \sin \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.904 |
|
| 8918 |
\begin{align*}
x^{2} \left (6+x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }+\left (2 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| 8919 |
\begin{align*}
3 x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| 8920 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{2}+\cos \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.905 |
|
| 8921 |
\begin{align*}
8 \left (-x^{3}+1\right ) y y^{\prime \prime }-4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}-12 x^{2} y y^{\prime }+3 x y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.905 |
|
| 8922 |
\begin{align*}
\left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 y^{\prime } x +10 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.905 |
|
| 8923 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{2 x}-\frac {\left (x +1\right ) y}{2 x^{2}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| 8924 |
\begin{align*}
n^{\prime }&=k n-b t \\
n \left (0\right ) &= n_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| 8925 |
\begin{align*}
z^{\prime }+4 i z&={\mathrm e}^{8 i t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| 8926 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.906 |
|
| 8927 |
\begin{align*}
y^{\prime }-2 y&=-10 \\
y \left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.906 |
|
| 8928 |
\begin{align*}
y^{\prime }+y-v^{\prime }-v&=0 \\
y^{\prime }+v^{\prime }-v&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.906 |
|
| 8929 |
\begin{align*}
x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (2 x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.907 |
|
| 8930 |
\begin{align*}
{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.907 |
|
| 8931 |
\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. |
✓ |
✓ |
✓ |
✓ |
0.907 |
|
| 8932 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.907 |
|
| 8933 |
\begin{align*}
4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| 8934 |
\begin{align*}
3 \left (x +3\right ) x^{2} y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| 8935 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.908 |
|
| 8936 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| 8937 |
\begin{align*}
x^{\prime }&=x-4 y+\cos \left (2 t \right ) \\
y^{\prime }&=x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| 8938 |
\begin{align*}
y y^{\prime }&=x +y^{2}-y^{2} {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.909 |
|
| 8939 |
\begin{align*}
2 x^{2} y^{\prime \prime }+\left (x^{2}+5 x \right ) y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.909 |
|
| 8940 |
\begin{align*}
y&=y^{\prime } \left (1+y^{\prime } \cos \left (y^{\prime }\right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.909 |
|
| 8941 |
\begin{align*}
\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (1+3 x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.909 |
|
| 8942 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| 8943 |
\begin{align*}
\left (2 x^{2}+4 y x -y^{2}\right ) y^{\prime }&=x^{2}-4 y x -2 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.911 |
|
| 8944 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (2 x \right ) \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 8945 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+5 \left (x +1\right ) y^{\prime }+\left (x^{2}-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 8946 |
\begin{align*}
y^{\prime \prime }&=\left (x^{2}+3\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.911 |
|
| 8947 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime } x +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.911 |
|
| 8948 |
\begin{align*}
y^{\prime \prime }+4 y&=\delta \left (t -4 \pi \right ) \\
y \left (0\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| 8949 |
\begin{align*}
\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime \prime }&=2 y x -{\mathrm e}^{y}-x \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.911 |
|
| 8950 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.912 |
|
| 8951 |
\begin{align*}
y^{\prime }&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.912 |
|
| 8952 |
\begin{align*}
2 y y^{\prime \prime }&=4 y^{2}+8 y^{3}+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.913 |
|
| 8953 |
\begin{align*}
y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| 8954 |
\begin{align*}
\left (x -2\right ) x y^{\prime \prime \prime }-x \left (x -2\right ) y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.913 |
|
| 8955 |
\begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| 8956 |
\begin{align*}
2 x^{\prime }-x+7 y^{\prime }+3 y&=90 \sin \left (2 t \right ) \\
x^{\prime }-5 x+8 y^{\prime }-3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| 8957 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2}+5 \,{\mathrm e}^{4 t} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| 8958 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.914 |
|
| 8959 |
\begin{align*}
y^{\prime \prime }-c \,x^{a} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.914 |
|
| 8960 |
\begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| 8961 |
\begin{align*}
{y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.915 |
|
| 8962 |
\begin{align*}
x^{n +1} y^{\prime }&=x^{2 n} a y^{2}+b \,x^{n} y+c \,x^{m}+d \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.915 |
|
| 8963 |
\begin{align*}
x^{\prime }&=-2 x-2 y+4 z \\
y^{\prime }&=-2 x+y+2 z \\
z^{\prime }&=-4 x-2 y+6 z+{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| 8964 |
\begin{align*}
y^{\prime \prime \prime }-7 y^{\prime \prime }+20 y^{\prime }-24 y&=-{\mathrm e}^{2 x} \left (\left (13-8 x \right ) \cos \left (2 x \right )-\left (8-4 x \right ) \sin \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.916 |
|
| 8965 |
\begin{align*}
\left (1-x \right ) x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-9 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.916 |
|
| 8966 |
\begin{align*}
a \left (2+a \right )^{2} y y^{\prime \prime }&=-a^{2} f \left (x \right )^{2} y^{4}+a^{2} \left (2+a \right ) y^{3} f^{\prime }\left (x \right )+a \left (2+a \right )^{2} f \left (x \right ) y^{2} y^{\prime }+\left (-1+a \right ) \left (2+a \right )^{2} {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
0.916 |
|
| 8967 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.916 |
|
| 8968 |
\begin{align*}
3 y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.916 |
|
| 8969 |
\begin{align*}
y^{\prime }&=2 y^{3}+t^{2} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.916 |
|
| 8970 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {2}{3}-3 x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| 8971 |
\begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| 8972 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| 8973 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.918 |
|
| 8974 |
\begin{align*}
\left (x y^{\prime \prime \prime }-y^{\prime \prime }\right )^{2}&={y^{\prime \prime \prime }}^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.918 |
|
| 8975 |
\begin{align*}
\left (-x^{2}+2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| 8976 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| 8977 |
\begin{align*}
y^{\prime \prime }&=2 y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.919 |
|
| 8978 |
\begin{align*}
9 x^{2} \left (x +5\right ) y^{\prime \prime }+9 x \left (5+9 x \right ) y^{\prime }-\left (5-8 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.919 |
|
| 8979 |
\begin{align*}
\left (a t +1\right ) y^{\prime }+y&=t \\
y \left (1\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.919 |
|
| 8980 |
\begin{align*}
5 {y^{\prime }}^{2}+6 y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.920 |
|
| 8981 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.920 |
|
| 8982 |
\begin{align*}
y^{\prime \prime }&=\left (\frac {x^{2}}{4}-\frac {11}{2}\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.920 |
|
| 8983 |
\begin{align*}
y^{\prime }&=\sin \left (y x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.920 |
|
| 8984 |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=\tan \left (t \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| 8985 |
\begin{align*}
\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| 8986 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| 8987 |
\begin{align*}
y^{\prime \prime }&=\cos \left (y x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} Series expansion around \(x=\frac {\pi }{2}\). |
✓ |
✓ |
✓ |
✗ |
0.921 |
|
| 8988 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| 8989 |
\begin{align*}
2 y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.921 |
|
| 8990 |
\begin{align*}
x^{2} \left (x +4\right ) y^{\prime \prime }+7 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| 8991 |
\begin{align*}
x -x^{2}-y^{2}+y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| 8992 |
\begin{align*}
{y^{\prime }}^{3}-\left (x +5\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.922 |
|
| 8993 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=39 \operatorname {Heaviside}\left (t \right )-507 \left (-2+t \right ) \operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| 8994 |
\begin{align*}
x^{\prime }&=-4 x+9 y+12 \,{\mathrm e}^{-t} \\
y^{\prime }&=-5 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| 8995 |
\begin{align*}
y^{\prime \prime \prime }+4 y^{\prime }&=\tan \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| 8996 |
\begin{align*}
y^{3} y^{\prime \prime }&=-1 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
0.922 |
|
| 8997 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| 8998 |
\begin{align*}
y^{\prime \prime }+3 t \left (1-t \right ) y^{\prime }+\frac {\left (1-{\mathrm e}^{t}\right ) y}{t}&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.923 |
|
| 8999 |
\begin{align*}
2 y^{\prime \prime }+y^{\prime }-4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| 9000 |
\begin{align*}
x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.924 |
|