| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 6901 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| 6902 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+20 y&={\mathrm e}^{2 x} \sin \left (4 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| 6903 |
\begin{align*}
y^{\prime }&=\left (-x^{2}+4\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| 6904 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| 6905 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{-t} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| 6906 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| 6907 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| 6908 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{-x} \sqrt {x +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| 6909 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| 6910 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\alpha ^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| 6911 |
\begin{align*}
5 y^{\prime \prime }+5 y^{\prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| 6912 |
\begin{align*}
\left (t^{2}+2\right ) y^{\prime \prime }-t y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| 6913 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2} \\
x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| 6914 |
\begin{align*}
y^{\prime \prime }&=\sin \left (y\right ) \\
y \left (0\right ) &= \frac {\pi }{4} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.520 |
|
| 6915 |
\begin{align*}
y^{\prime \prime }-16 y&=40 \,{\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| 6916 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=100 \cos \left (4 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| 6917 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }-5 y&=0 \\
y \left (-1\right ) &= 3 \\
y^{\prime }\left (-1\right ) &= 9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| 6918 |
\begin{align*}
y^{\prime \prime }+2 y&={\mathrm e}^{x}+2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| 6919 |
\begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.520 |
|
| 6920 |
\begin{align*}
y^{\prime \prime }+2 i y^{\prime }+y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| 6921 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.520 |
|
| 6922 |
\begin{align*}
y^{\prime }&=\frac {x}{\sqrt {x^{2}+5}} \\
y \left (2\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| 6923 |
\begin{align*}
y^{\prime }-y \,{\mathrm e}^{x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| 6924 |
\begin{align*}
y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.520 |
|
| 6925 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+4 y&={\mathrm e}^{x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| 6926 |
\begin{align*}
{y^{\prime }}^{2}+x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| 6927 |
\begin{align*}
\left (x^{2}-2 y x \right ) {y^{\prime }}^{2}-\left (3 x^{2}+2 y\right ) \left (x -2 y\right ) y^{\prime }+6 x y \left (x -2 y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| 6928 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
y^{\prime \prime }\left (0\right ) &= -4 \\
y^{\prime \prime \prime }\left (0\right ) &= 12 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| 6929 |
\begin{align*}
x^{3} y^{\prime \prime \prime }&=1+\sqrt {x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| 6930 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-2 y&=x^{2}+4 x +3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| 6931 |
\begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2} \\
y_{2}^{\prime }&=y_{1}-y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| 6932 |
\begin{align*}
z^{\prime \prime }-2 z^{\prime }-2 z&=0 \\
z \left (0\right ) &= 0 \\
z^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| 6933 |
\begin{align*}
y^{\prime }&=3 \sqrt {x +3} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| 6934 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| 6935 |
\begin{align*}
{y^{\prime }}^{2} \left (x^{2}-1\right )-2 x y y^{\prime }+y^{2}-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.521 |
|
| 6936 |
\begin{align*}
y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| 6937 |
\begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| 6938 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+p^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| 6939 |
\begin{align*}
{y^{\prime }}^{2}-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| 6940 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2} \\
x_{2}^{\prime }&=4 x_{1}+x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| 6941 |
\begin{align*}
f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \\
\end{align*}
Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| 6942 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| 6943 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| 6944 |
\begin{align*}
y^{\prime \prime }-y^{\prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| 6945 |
\begin{align*}
x^{\prime }&=2 x+y-z \\
y^{\prime }&=-x+2 z \\
z^{\prime }&=-x-2 y+4 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| 6946 |
\begin{align*}
6 x y^{\prime \prime }+6 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| 6947 |
\begin{align*}
9 y^{\prime \prime }-24 y^{\prime }+16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| 6948 |
\begin{align*}
y^{\prime \prime }-4 y&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| 6949 |
\begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=-5 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| 6950 |
\begin{align*}
t^{2} y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| 6951 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| 6952 |
\begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+\left (x -2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6953 |
\begin{align*}
\left (x -2\right )^{2} y^{\prime \prime }-\left (x^{2}-4\right ) y^{\prime }+\left (x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6954 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-3 x_{2} \\
x_{2}^{\prime }&=6 x_{1}-7 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 8 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6955 |
\begin{align*}
x_{1}^{\prime }&=7 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=4 x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6956 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6957 |
\begin{align*}
x y^{\prime }+y&=x^{4} y^{4} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6958 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6959 |
\begin{align*}
y+3 x y^{\prime }+9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6960 |
\begin{align*}
y^{\prime }-y x&=\sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6961 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6962 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6963 |
\begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=9 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6964 |
\begin{align*}
\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.523 |
|
| 6965 |
\begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=2 x-4 y \\
z^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6966 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6967 |
\begin{align*}
y^{\prime }&=\frac {2 x^{2}-x +1}{\left (x -1\right ) \left (x^{2}+1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6968 |
\begin{align*}
\sin \left (y \right )^{2}&=x^{\prime } \\
x \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6969 |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }+10 y&={\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6970 |
\begin{align*}
\frac {x^{\prime \prime }}{4}+2 x^{\prime }+x&=0 \\
x \left (0\right ) &= -{\frac {1}{2}} \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6971 |
\begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6972 |
\begin{align*}
y^{\prime } \left (y^{\prime }+y\right )&=x \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.523 |
|
| 6973 |
\begin{align*}
\left (x +3\right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6974 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=2 \cos \left (x \right )+4 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6975 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=4 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6976 |
\begin{align*}
4 y^{\prime \prime }+y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6977 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\left (x -2\right ) {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6978 |
\begin{align*}
\left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6979 |
\begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6980 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6981 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6982 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=2 x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6983 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+10 y&=3 x \,{\mathrm e}^{-3 x}-2 \,{\mathrm e}^{3 x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| 6984 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } \left (x^{2}+2\right )+y x&=0 \\
y \left (0\right ) &= -3 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| 6985 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=x +{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| 6986 |
\begin{align*}
\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.524 |
|
| 6987 |
\begin{align*}
x^{\prime \prime }-2 x^{\prime }+2 x&={\mathrm e}^{-t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| 6988 |
\begin{align*}
y&=y y^{\prime }+y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| 6989 |
\begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| 6990 |
\begin{align*}
x^{\prime }&=-y+z \\
y^{\prime }&=-x+z \\
z^{\prime }&=z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| 6991 |
\begin{align*}
y^{\prime }+y \,{\mathrm e}^{2 x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| 6992 |
\begin{align*}
x^{\prime }&=-3 x+\frac {5 y}{2} \\
y^{\prime }&=-\frac {5 x}{2}+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| 6993 |
\begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=-\frac {3 x}{4}-\frac {y}{4} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| 6994 |
\begin{align*}
y^{\prime }&=x \,{\mathrm e}^{x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| 6995 |
\begin{align*}
x^{\prime }&=-2 x-3 y \\
y^{\prime }&=-3 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| 6996 |
\begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| 6997 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=\sin \left (2 x \right ) {\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| 6998 |
\begin{align*}
x_{1}^{\prime }&=\frac {3 x_{1}}{4}-2 x_{2} \\
x_{2}^{\prime }&=x_{1}-\frac {5 x_{2}}{4} \\
\end{align*} |
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0.525 |
|
| 6999 |
\begin{align*}
y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y&=0 \\
y \left (-1\right ) &= 0 \\
y^{\prime }\left (-1\right ) &= 1 \\
\end{align*}
Series expansion around \(t=-1\). |
✓ |
✓ |
✓ |
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0.525 |
|
| 7000 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-2 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.525 |
|