| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 11901 |
\begin{align*}
x^{\prime \prime }-2 x&=2 \,{\mathrm e}^{t} \\
x \left (0\right ) &= 0 \\
x \left (a \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| 11902 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| 11903 |
\begin{align*}
2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| 11904 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x \left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| 11905 |
\begin{align*}
y^{\prime \prime }-8 y^{\prime }+17 y&={\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 11906 |
\begin{align*}
4 y+y^{\prime \prime }&=x \sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 11907 |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}+x^{2} \left (x -y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.665 |
|
| 11908 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=\cos \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.665 |
|
| 11909 |
\begin{align*}
x^{\prime }&=8 x+2 y-17 \\
y^{\prime }&=4 x+y-13 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 11910 |
\begin{align*}
y^{3} y^{\prime \prime }&=-1 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
0.665 |
|
| 11911 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 11912 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 11913 |
\begin{align*}
y^{\prime \prime } x -\left (2 x -1\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 11914 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x +1 \\
y \left (0\right ) &= 1 \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 11915 |
\begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 11916 |
\begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.665 |
|
| 11917 |
\begin{align*}
y^{\prime \prime }&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 11918 | \begin{align*}
y_{1}^{\prime }&=-y_{1}+y_{2}-y_{3} \\
y_{2}^{\prime }&=-2 y_{1}+2 y_{3} \\
y_{3}^{\prime }&=-y_{1}+3 y_{2}-y_{3} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.666 |
|
| 11919 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| 11920 |
\begin{align*}
y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| 11921 |
\begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| 11922 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| 11923 |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=x_{3} \\
x_{3}^{\prime }&=6 t \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| 11924 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| 11925 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+3 x_{2}+7 x_{3} \\
x_{2}^{\prime }&=-x_{2}-4 x_{3} \\
x_{3}^{\prime }&=x_{2}+3 x_{3} \\
x_{4}^{\prime }&=-6 x_{2}-14 x_{3}+x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 11926 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 11927 |
\begin{align*}
\left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 11928 |
\begin{align*}
2 y+3 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 11929 |
\begin{align*}
y^{\prime \prime } x +3 y^{\prime }+x^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 11930 |
\begin{align*}
2 y^{3}+\left (4 x^{3} y^{3}-3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.667 |
|
| 11931 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+50 y&={\mathrm e}^{-t} \csc \left (7 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 11932 |
\begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right . \\
y \left (\pi \right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 11933 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} 0 & 0\le t <2 \\ 4 & 2\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✗ |
✓ |
✗ |
0.667 |
|
| 11934 |
\begin{align*}
y^{\prime }-5 y&=3 \operatorname {Heaviside}\left (t -4\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 11935 |
\begin{align*}
y^{\prime }&=y-x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 11936 |
\begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+9 y^{\prime }-10 y&=10 \,{\mathrm e}^{2 x}+20 \,{\mathrm e}^{x} \sin \left (2 x \right )-10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 11937 | \begin{align*}
y_{1}^{\prime }&=\frac {y_{1}}{3}+\frac {y_{2}}{3}-y_{3} \\
y_{2}^{\prime }&=-\frac {4 y_{1}}{3}-\frac {4 y_{2}}{3}+y_{3} \\
y_{3}^{\prime }&=-\frac {2 y_{1}}{3}+\frac {y_{2}}{3} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.668 |
|
| 11938 |
\begin{align*}
y^{\prime \prime }+t y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.668 |
|
| 11939 |
\begin{align*}
\left (y^{2}+x^{2}\right ) y^{\prime }+2 x \left (2 x +y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.668 |
|
| 11940 |
\begin{align*}
\left (x^{2}-4 y^{2}\right ) {y^{\prime }}^{2}+6 x y^{\prime } y-4 x^{2}+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.668 |
|
| 11941 |
\begin{align*}
\left (-2 x^{3}+1\right ) y-x \left (-2 x^{3}+1\right ) y^{\prime }+x^{5} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.668 |
|
| 11942 |
\begin{align*}
x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 11943 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=25 t -100 \delta \left (t -\pi \right ) \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 11944 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 11945 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x^{2}-3\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 11946 |
\begin{align*}
y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 11947 |
\begin{align*}
x^{\prime }&=-3 x-3 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 11948 |
\begin{align*}
y^{\prime \prime }+3 y&=\operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 11949 |
\begin{align*}
y y^{\prime \prime }+2 {y^{\prime }}^{2}&=3 y^{\prime } y \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= {\frac {3}{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.668 |
|
| 11950 |
\begin{align*}
x^{\prime }&=2 x-y+z \\
y^{\prime }&=x+z \\
z^{\prime }&=y-2 z-3 x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 11951 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=-8 x_{1}-5 x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 11952 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 11953 |
\begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=24 \cos \left (x \right ) x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 11954 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=20 \,{\mathrm e}^{-2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 11955 |
\begin{align*}
t^{2} x^{\prime \prime }+3 t x^{\prime }&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 11956 | \begin{align*}
y^{2} {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 0.669 |
|
| 11957 |
\begin{align*}
\left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (5 x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| 11958 |
\begin{align*}
3 x {y^{\prime }}^{2}-6 y^{\prime } y+x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| 11959 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| 11960 |
\begin{align*}
t x^{\prime \prime }&=x^{\prime } \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| 11961 |
\begin{align*}
-x^{2} y+\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| 11962 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime \prime }-y^{\prime } x +2 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| 11963 |
\begin{align*}
{y^{\prime \prime }}^{3}&=12 y^{\prime } \left (-2 y^{\prime }+y^{\prime \prime } x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.670 |
|
| 11964 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x -x^{4}-6&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.670 |
|
| 11965 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+34 y&={\mathrm e}^{3 t} \tan \left (5 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| 11966 |
\begin{align*}
\left (x^{2}-25\right )^{2} y^{\prime \prime }-\left (x +5\right ) y^{\prime }+10 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| 11967 |
\begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.670 |
|
| 11968 |
\begin{align*}
x^{\prime }+2 x-3 y&=t \\
y^{\prime }-3 x+2 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| 11969 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y+8 \,{\mathrm e}^{-x}+3 x&=0 \\
y \left (0\right ) &= -{\frac {2}{3}} \\
y \left (1\right ) &= 2 \,{\mathrm e}^{-1}+\frac {1}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| 11970 |
\begin{align*}
y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| 11971 |
\begin{align*}
x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 11972 |
\begin{align*}
\left (x +3\right ) x^{2} y^{\prime \prime }+x \left (5+4 x \right ) y^{\prime }-\left (1-2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 11973 |
\begin{align*}
t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 11974 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime }+y&=x \\
y^{\prime }\left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.671 |
|
| 11975 | \begin{align*}
y^{\prime \prime }&=\frac {c y}{\left (x -a \right )^{2} \left (-b +x \right )^{2}} \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 0.671 |
|
| 11976 |
\begin{align*}
{y^{\prime }}^{2}-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 11977 |
\begin{align*}
x^{\prime \prime }+\omega ^{2} x&=\sin \left (\alpha t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 11978 |
\begin{align*}
{y^{\prime }}^{2}-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 11979 |
\begin{align*}
y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 11980 |
\begin{align*}
{y^{\prime \prime \prime }}^{2}&={y^{\prime \prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 11981 |
\begin{align*}
y^{\prime \prime }-2 a y^{\prime }+a^{2} y&={\mathrm e}^{a x}+f^{\prime \prime }\left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 11982 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 11983 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 11984 |
\begin{align*}
f \left (x \right ) y^{\prime }+g \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 11985 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 11986 |
\begin{align*}
x^{\prime }-y^{\prime }&=x+y-t \\
2 x^{\prime }+3 y^{\prime }&=2 x+6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 11987 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=x^{3}+3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 11988 |
\begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 11989 |
\begin{align*}
5 y^{\prime \prime } x +\left (30+3 x \right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 11990 |
\begin{align*}
2 \left (x +3\right ) x^{2} y^{\prime \prime }+x \left (5 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 11991 |
\begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+17 y&=g \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 11992 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x} \cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 11993 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-\left (4 x^{2}-3 x -5\right ) y^{\prime }+\left (4 x^{2}-6 x -5\right ) y&={\mathrm e}^{2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.673 |
|
| 11994 | \begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \sin \left (x \right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.673 |
|
| 11995 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-p^{2}+x^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.673 |
|
| 11996 |
\begin{align*}
y_{1}^{\prime }&=-y_{1}+2 y_{2}+5 \\
y_{2}^{\prime }&=-2 y_{1}-y_{2} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 11997 |
\begin{align*}
\left (x +3\right ) x^{2} y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 11998 |
\begin{align*}
t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 11999 |
\begin{align*}
y^{\prime \prime }+y&=2 \sin \left (x \right )-3 \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 12000 |
\begin{align*}
a^{4} y+2 a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=\cosh \left (a x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|