| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12901 |
\begin{align*}
6 y-4 \left (x +1\right ) y^{\prime }+\left (x +1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| 12902 |
\begin{align*}
\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| 12903 |
\begin{align*}
y^{\prime \prime }&=-\frac {a y}{\left (x^{2}-1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| 12904 |
\begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x -7 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| 12905 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| 12906 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=x^{2} {\mathrm e}^{-x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| 12907 |
\begin{align*}
y^{\prime \prime }-10 y^{\prime }+29 y&=8 \,{\mathrm e}^{5 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| 12908 |
\begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=4 x+5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| 12909 |
\begin{align*}
x^{\prime }&=\frac {\cos \left (t \right )}{\sin \left (t \right )} \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| 12910 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| 12911 |
\begin{align*}
-y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.118 |
|
| 12912 |
\begin{align*}
y-y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.118 |
|
| 12913 |
\begin{align*}
\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime \prime }-a \,\lambda ^{2} {\mathrm e}^{\lambda x} y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.118 |
|
| 12914 |
\begin{align*}
y^{\prime \prime }+16 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| 12915 |
\begin{align*}
y&=x \left (1+y^{\prime }\right )+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| 12916 |
\begin{align*}
y^{\prime }&=\frac {x^{2}-1}{1+y^{2}} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.119 |
|
| 12917 |
\begin{align*}
y^{\prime }+2 y&=-6 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.119 |
|
| 12918 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.120 |
|
| 12919 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (3+2 x \right ) y^{\prime }+\left (1+3 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.120 |
|
| 12920 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right . \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.120 |
|
| 12921 |
\begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=-3 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.120 |
|
| 12922 |
\begin{align*}
y^{\prime \prime }+7 y^{\prime }+6 y&=250 \,{\mathrm e}^{t} \cos \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -7 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.120 |
|
| 12923 |
\begin{align*}
2 t^{2} y^{\prime \prime }+3 y^{\prime } t -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.121 |
|
| 12924 |
\begin{align*}
2 x^{2} y^{\prime \prime }+x \left (4 x -1\right ) y^{\prime }+2 \left (3 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.121 |
|
| 12925 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.122 |
|
| 12926 |
\begin{align*}
y^{\prime }-\cos \left (a y+b x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.122 |
|
| 12927 |
\begin{align*}
-y+y^{\prime } x&=\left (x -1\right ) \left (y^{\prime \prime }-x +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.122 |
|
| 12928 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.122 |
|
| 12929 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.122 |
|
| 12930 |
\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 \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.122 |
|
| 12931 |
\begin{align*}
g \left (x , y\right )+f \left (x , y\right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.123 |
|
| 12932 |
\begin{align*}
x \left (x -2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
1.123 |
|
| 12933 |
\begin{align*}
2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.123 |
|
| 12934 |
\begin{align*}
p^{\prime }&=p-p^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.124 |
|
| 12935 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}+2 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{2}-4 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-4 x_{2}+2 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.124 |
|
| 12936 |
\begin{align*}
y^{\prime }&=\left (4 x +y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.125 |
|
| 12937 |
\begin{align*}
y^{\prime } \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.125 |
|
| 12938 |
\begin{align*}
x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.125 |
|
| 12939 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.125 |
|
| 12940 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a^{2} x^{2}-6\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.125 |
|
| 12941 |
\begin{align*}
\left (-x^{2}+4 x -3\right ) y^{\prime \prime }-2 \left (x -2\right ) y^{\prime }+6 y&=0 \\
y \left (2\right ) &= 1 \\
y^{\prime }\left (2\right ) &= 0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
1.125 |
|
| 12942 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.126 |
|
| 12943 |
\begin{align*}
y^{\prime }&=\sqrt {\left (y+2\right ) \left (-1+y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.126 |
|
| 12944 |
\begin{align*}
y^{\prime \prime }+a^{2} y&=\delta \left (x -\pi \right ) f \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.126 |
|
| 12945 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{2}-x_{3} \\
x_{2}^{\prime }&=x_{1}-x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}-2 x_{2}-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.126 |
|
| 12946 |
\begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }-4 \left (x -1\right ) y^{\prime }-14 y&=x^{3}-3 x^{2}+3 x -8 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.126 |
|
| 12947 |
\begin{align*}
x^{\prime }+y&=4 \\
x-y^{\prime }&=3 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.126 |
|
| 12948 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.127 |
|
| 12949 |
\begin{align*}
\left (t^{2}+9\right ) y^{\prime \prime }+2 y^{\prime } t&=0 \\
y \left (3\right ) &= 2 \pi \\
y^{\prime }\left (3\right ) &= {\frac {2}{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.127 |
|
| 12950 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=\ln \left (x \right ) \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✗ |
1.127 |
|
| 12951 |
\begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.128 |
|
| 12952 |
\begin{align*}
x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}-25\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.128 |
|
| 12953 |
\begin{align*}
y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.128 |
|
| 12954 |
\begin{align*}
y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x \left (a^{2}-x^{2}\right )}&=\frac {x^{2}}{a \left (a^{2}-x^{2}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.128 |
|
| 12955 |
\begin{align*}
y^{\prime \prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.129 |
|
| 12956 |
\begin{align*}
\left (a^{2}-y^{2}\right ) {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.129 |
|
| 12957 |
\begin{align*}
y^{\prime \prime }&=6 \,{\mathrm e}^{x} \sin \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.129 |
|
| 12958 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.129 |
|
| 12959 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{a x} \\
y \left (0\right ) &= y_{0} \\
y^{\prime }\left (0\right ) &= y_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.129 |
|
| 12960 |
\begin{align*}
y^{\prime }-m y&=c \,{\mathrm e}^{x m} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.129 |
|
| 12961 |
\begin{align*}
x^{\prime }+2 x-y&=100 \sin \left (t \right ) \\
y^{\prime }-4 x-y&=36 t \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= -8 \\
y \left (0\right ) &= -21 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.130 |
|
| 12962 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (1\right ) &= 7 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.131 |
|
| 12963 |
\begin{align*}
y^{\prime \prime }-9 y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 15 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.132 |
|
| 12964 |
\begin{align*}
t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.132 |
|
| 12965 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=\delta \left (t -\frac {\pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.132 |
|
| 12966 |
\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*} |
✓ |
✓ |
✓ |
✓ |
1.132 |
|
| 12967 |
\begin{align*}
2 \left (x +5\right ) y-x \left (7+2 x \right ) y^{\prime }+2 x^{2} y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.132 |
|
| 12968 |
\begin{align*}
y^{\prime \prime }+2 a x y^{\prime }+y a^{2} x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.132 |
|
| 12969 |
\begin{align*}
y^{\prime }&=a y+b \\
y \left (c \right ) &= d \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.132 |
|
| 12970 |
\begin{align*}
4 y^{\prime \prime }-3 y^{\prime }-y&=34 \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.132 |
|
| 12971 |
\begin{align*}
a y^{2}+x^{3} y^{\prime } y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
1.133 |
|
| 12972 |
\begin{align*}
{y^{\prime }}^{2}-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.133 |
|
| 12973 |
\begin{align*}
x \left (1-2 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+4 \ln \left (x \right ) x^{2}\right ) y^{\prime }-\left (2+4 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.133 |
|
| 12974 |
\begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.134 |
|
| 12975 |
\begin{align*}
5 y^{\prime \prime } x +8 y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.134 |
|
| 12976 |
\begin{align*}
\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (2+x \right ) y&=x \left (x +1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.134 |
|
| 12977 |
\begin{align*}
t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
1.135 |
|
| 12978 |
\begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.135 |
|
| 12979 |
\begin{align*}
{y^{\prime \prime }}^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.135 |
|
| 12980 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{2}+x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.135 |
|
| 12981 |
\begin{align*}
y^{\prime \prime }&=-\frac {x \sin \left (x \right ) y^{\prime }}{\cos \left (x \right ) x -\sin \left (x \right )}+\frac {\sin \left (x \right ) y}{\cos \left (x \right ) x -\sin \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.135 |
|
| 12982 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-8\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.135 |
|
| 12983 |
\begin{align*}
5 {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.136 |
|
| 12984 |
\begin{align*}
4 y x -\left (x^{2}+7\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.136 |
|
| 12985 |
\begin{align*}
x^{4} y^{\prime \prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.136 |
|
| 12986 |
\begin{align*}
t^{2} y^{\prime \prime }+t \,{\mathrm e}^{t} y^{\prime }+4 \left (1-4 t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
1.136 |
|
| 12987 |
\begin{align*}
y^{\prime \prime }&=2 y y^{\prime } \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.137 |
|
| 12988 |
\begin{align*}
2 x +3 y+4+\left (3 x +4 y+5\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.137 |
|
| 12989 |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.137 |
|
| 12990 |
\begin{align*}
y^{\prime \prime }&=2 y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.138 |
|
| 12991 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=10 \sin \left (t \right )+10 \delta \left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.138 |
|
| 12992 |
\begin{align*}
{y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.138 |
|
| 12993 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=-x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.138 |
|
| 12994 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-15 y&=16 t \,{\mathrm e}^{-t}-15 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -9 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.138 |
|
| 12995 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x \left (x -2\right ) y^{\prime }+2 \left (2-3 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.139 |
|
| 12996 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.139 |
|
| 12997 |
\begin{align*}
y^{\prime \prime } x +\left (-x +2\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.139 |
|
| 12998 |
\begin{align*}
y^{\prime \prime } x +4 y^{\prime }&=18 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.139 |
|
| 12999 |
\begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
1.140 |
|
| 13000 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.140 |
|