| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 7901 |
\begin{align*}
x^{\prime }&=2 x-3 y+2 \sin \left (2 t \right ) \\
y^{\prime }&=x-2 y-\cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 7902 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}+5 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-6 x_{1}-6 x_{2}-5 x_{3} \\
x_{3}^{\prime }&=6 x_{1}+6 x_{2}+5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 7903 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+\sqrt {3}\, x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=\sqrt {3}\, x_{1}-x_{2}+\sqrt {3}\, {\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 7904 |
\begin{align*}
y^{\prime \prime }-9 y&={\mathrm e}^{3 x}+\sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 7905 |
\begin{align*}
a^{2} y+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 7906 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 7907 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +y {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.003 |
|
| 7908 |
\begin{align*}
y^{\prime \prime }-y&=\frac {2}{{\mathrm e}^{x}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 7909 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 7910 |
\begin{align*}
\left (-y+y^{\prime } x \right )^{3}+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.004 |
|
| 7911 |
\begin{align*}
y^{\prime \prime }+8 y^{\prime }+20 y&=\sin \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 7912 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 7913 |
\begin{align*}
\left (-y^{\prime } x +y\right ) \left (y^{\prime }-1\right )&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.004 |
|
| 7914 |
\begin{align*}
y^{\prime }+2 \left (-1+x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| 7915 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+4 x&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| 7916 |
\begin{align*}
y^{\prime \prime \prime }-y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
y^{\prime \prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| 7917 |
\begin{align*}
1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| 7918 |
\begin{align*}
x^{\prime }&=x-5 y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| 7919 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+2 x_{2}-x_{3} \\
x_{2}^{\prime }&=-2 x_{1}+3 x_{2}-2 x_{3} \\
x_{3}^{\prime }&=-2 x_{1}+4 x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| 7920 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-y^{\prime } x +y&=\ln \left (x \right )+x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| 7921 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| 7922 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 7923 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+x&=5 \sin \left (7 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 7924 |
\begin{align*}
x^{\prime \prime }-x&={\mathrm e}^{t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 7925 |
\(\left [\begin {array}{ccc} -5 & -12 & 6 \\ 1 & 5 & -1 \\ -7 & -10 & 8 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
1.007 |
|
| 7926 |
\begin{align*}
{y^{\prime }}^{2} \left (x^{2}-1\right )-2 y y^{\prime } x +y^{2}-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.007 |
|
| 7927 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=2 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 7928 |
\begin{align*}
2 y^{\prime \prime }-3 y^{2}&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.007 |
|
| 7929 |
\begin{align*}
y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (a -1\right ) b +a \,x^{2}+\left (1-a \right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.008 |
|
| 7930 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+x&=4 t +5 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| 7931 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| 7932 |
\begin{align*}
y_{1}^{\prime }&=-3 y_{1}+3 y_{2}+y_{3} \\
y_{2}^{\prime }&=y_{1}-5 y_{2}-3 y_{3} \\
y_{3}^{\prime }&=-3 y_{1}+7 y_{2}+3 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| 7933 |
\begin{align*}
y^{\prime \prime }&=-\frac {y^{\prime }}{x^{3}}+\frac {2 y}{x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.009 |
|
| 7934 |
\begin{align*}
y^{\prime \prime } x +\left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.009 |
|
| 7935 |
\begin{align*}
y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.009 |
|
| 7936 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=x^{3}+3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| 7937 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }-5 y&={\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| 7938 |
\begin{align*}
m x^{\prime \prime }+k x&=F_{0} \cos \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| 7939 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}+6 x_{3} \\
x_{2}^{\prime }&=-2 x_{1}+x_{2}-2 x_{3} \\
x_{3}^{\prime }&=-x_{1}-2 x_{2}-4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| 7940 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| 7941 |
\begin{align*}
y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| 7942 |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.010 |
|
| 7943 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| 7944 |
\begin{align*}
y^{\prime \prime }-2 m y^{\prime }+m^{2} y&=\sin \left (x n \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| 7945 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| 7946 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=10 x^{3} {\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| 7947 |
\begin{align*}
y^{\prime }+z^{\prime }+6 y&=0 \\
z^{\prime }+5 y+z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| 7948 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 7949 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 7950 |
\begin{align*}
t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-t y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 7951 |
\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ -2 & 4 & -1 \\ -4 & 4 & 1 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
1.011 |
|
| 7952 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-12 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 7953 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=t +2 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 7954 |
\begin{align*}
x^{\prime \prime }+t x^{\prime }&=t^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.012 |
|
| 7955 |
\begin{align*}
x^{2} y^{\prime }&=x^{3} \sin \left (3 x \right )+4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.012 |
|
| 7956 |
\begin{align*}
y^{\prime }&=\frac {x}{\sqrt {x^{2}+5}} \\
y \left (2\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.012 |
|
| 7957 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}+6 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-2 x_{1}-2 x_{2}-x_{3} \\
x_{3}^{\prime }&=-2 x_{1}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.012 |
|
| 7958 |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+\sin \left (x \right ) y&=0 \\
y \left (0\right ) &= a_{0} \\
y^{\prime }\left (0\right ) &= a_{1} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 7959 |
\begin{align*}
2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 7960 |
\begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+32 y^{\prime \prime }-64 y^{\prime }+64 y&={\mathrm e}^{2 x} \left (\cos \left (2 x \right )-\sin \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 7961 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 7962 |
\begin{align*}
{y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 7963 |
\begin{align*}
y^{\prime \prime }+y&=x^{2}+x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 7964 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 7965 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 7966 |
\begin{align*}
a y^{\prime \prime }+b y^{\prime }+c y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 7967 |
\begin{align*}
\frac {31 y^{\prime \prime \prime }}{100}+\frac {56 y^{\prime \prime }}{5}-\frac {49 y^{\prime }}{5}+\frac {53 y}{10}&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= -1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.013 |
|
| 7968 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{3} \\
x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 7969 |
\begin{align*}
y^{\prime }&=\frac {1}{\sqrt {-x^{2}+1}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 7970 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 9 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 7971 |
\begin{align*}
28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.014 |
|
| 7972 |
\begin{align*}
y^{\prime }-y x&=\sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.014 |
|
| 7973 |
\begin{align*}
3 {y^{\prime }}^{3}-x^{4} y^{\prime }+2 x^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.015 |
|
| 7974 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{-2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.015 |
|
| 7975 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-18 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-9 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.015 |
|
| 7976 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2+{\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.015 |
|
| 7977 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.016 |
|
| 7978 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+17 y&=\frac {64 \,{\mathrm e}^{-x}}{3+\sin \left (4 x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.016 |
|
| 7979 |
\begin{align*}
3 y y^{\prime }+y^{\prime \prime }&=f \left (x \right )+g \left (x \right ) y-y^{3} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.016 |
|
| 7980 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| 7981 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+x&=t^{2} {\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| 7982 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| 7983 |
\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & 1 & -1 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
1.016 |
|
| 7984 |
\begin{align*}
x^{\prime }&=x+2 y+4 \\
y^{\prime }&=-2 x+y-3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| 7985 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }-12 y&=\left (-1+x \right ) {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| 7986 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 y+z \\
z^{\prime }&=x+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| 7987 |
\begin{align*}
y^{\prime \prime }&=2 a y^{\prime }-\left (a^{2}-\omega ^{2}\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| 7988 |
\begin{align*}
y^{\left (6\right )}+y^{\prime \prime \prime \prime }-y&=4 x^{5}-6 x^{2}+2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| 7989 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 7990 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x^{5}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 7991 |
\begin{align*}
y^{2}-\frac {y}{x \left (x +y\right )}+2+\left (\frac {1}{x +y}+2 \left (x +1\right ) y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.017 |
|
| 7992 |
\begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=5 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 7993 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+3 x&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 7994 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 7995 |
\begin{align*}
{y^{\prime \prime }}^{2}-2 y^{\prime \prime } x -y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.017 |
|
| 7996 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{\frac {5 x}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 7997 |
\begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 7998 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-12 y&={\mathrm e}^{x} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 7999 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 8000 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.018 |
|