| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 13901 |
\begin{align*}
x^{\prime }&=-x-y \\
y^{\prime }&=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\
z^{\prime }&=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.385 |
|
| 13902 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.385 |
|
| 13903 |
\begin{align*}
y^{\prime }&=1+\cos \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.385 |
|
| 13904 |
\begin{align*}
7 y^{\prime \prime }-y^{\prime }&=14 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.385 |
|
| 13905 |
\begin{align*}
4 x^{2} y^{\prime \prime }+3 x^{2} y^{\prime }+\left (1+3 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.386 |
|
| 13906 |
\begin{align*}
2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.386 |
|
| 13907 |
\begin{align*}
y^{\prime }&=\frac {1}{y} \\
y \left (-2\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.387 |
|
| 13908 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (-3 x^{2}+x \right ) y^{\prime }+y \,{\mathrm e}^{x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.387 |
|
| 13909 |
\begin{align*}
4 x y^{\prime \prime }+2 y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.387 |
|
| 13910 |
\begin{align*}
4 \left (1-y\right ) y y^{\prime \prime }&=3 \left (-2 y+1\right ) {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.388 |
|
| 13911 |
\begin{align*}
\sin \left (x \right ) u^{\prime \prime }+2 \cos \left (x \right ) u^{\prime }+\sin \left (x \right ) u&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.388 |
|
| 13912 |
\begin{align*}
a y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.389 |
|
| 13913 |
\begin{align*}
a y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.389 |
|
| 13914 |
\begin{align*}
x \left (a \,x^{2}+b \right ) y^{\prime \prime }+2 \left (a \,x^{2}+b \right ) y^{\prime }-2 a x y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.390 |
|
| 13915 |
\begin{align*}
-12 y-8 x y^{\prime }+\left (a^{2}-x^{2}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.391 |
|
| 13916 |
\begin{align*}
2 x \left (1-x \right ) y^{\prime \prime }-\left (1+6 x \right ) y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.391 |
|
| 13917 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }+\left (x +1\right ) x y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.391 |
|
| 13918 |
\begin{align*}
x^{\prime }&=\sec \left (t \right )^{2} \\
x \left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.391 |
|
| 13919 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{2}+2 x -6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.391 |
|
| 13920 |
\begin{align*}
x^{\prime }&=-x+y+z+{\mathrm e}^{t} \\
y^{\prime }&=x-y+z+{\mathrm e}^{3 t} \\
z^{\prime }&=x+y+z+4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.391 |
|
| 13921 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (t \right ) \cos \left (2 t \right ) \cos \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.392 |
|
| 13922 |
\begin{align*}
-2 \left (1-x \right ) y+2 \left (-x +3\right ) x \left (x +1\right ) y^{\prime }+\left (1-x \right ) x \left (x +1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.392 |
|
| 13923 |
\begin{align*}
4 x^{2} y^{\prime \prime }-x^{2} y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.392 |
|
| 13924 |
\begin{align*}
y \left (2 x -y-1\right )+x \left (2 y-x -1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.393 |
|
| 13925 |
\begin{align*}
y \left (3-4 y\right )^{2} {y^{\prime }}^{2}&=4-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.393 |
|
| 13926 |
\begin{align*}
x^{\prime \prime }+x&=2 \tan \left (t \right ) \\
x \left (0\right ) &= 4 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.393 |
|
| 13927 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x +{\mathrm e}^{-x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.393 |
|
| 13928 |
\begin{align*}
{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.393 |
|
| 13929 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \cos \left (2 x \right )+\sin \left (2 x \right )+2 \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.393 |
|
| 13930 |
\begin{align*}
y^{\prime \prime }-y^{\prime }&={\mathrm e}^{x} \left (x^{2}+10\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.394 |
|
| 13931 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+a \,{\mathrm e}^{-2 x} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.394 |
|
| 13932 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=1+2 \cos \left (x \right )+\cos \left (2 x \right )-\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.394 |
|
| 13933 |
\begin{align*}
\left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2}}{a}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.394 |
|
| 13934 |
\begin{align*}
a \left (x y^{\prime }-y\right )^{2}+x^{2} y^{\prime \prime }&=b \,x^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.395 |
|
| 13935 |
\begin{align*}
y^{\prime }+y \sqrt {1+\sin \left (x \right )^{2}}&=x \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.395 |
|
| 13936 |
\begin{align*}
{y^{\prime }}^{3}-{y^{\prime }}^{2}+x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.395 |
|
| 13937 |
\begin{align*}
y^{\prime \prime }&=\frac {3 y}{4 \left (x^{2}+x +1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.395 |
|
| 13938 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.395 |
|
| 13939 |
\begin{align*}
4 y+y^{\prime \prime }&=4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.396 |
|
| 13940 |
\begin{align*}
2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.396 |
|
| 13941 |
\begin{align*}
y^{\prime }-3 y&=6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.396 |
|
| 13942 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }+\left (2-4 x \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.396 |
|
| 13943 |
\begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }-2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.397 |
|
| 13944 |
\begin{align*}
\left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.397 |
|
| 13945 |
\begin{align*}
y^{\prime \prime }+4 y&=8 \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.398 |
|
| 13946 |
\begin{align*}
\left (x^{4}+2 x^{2}+a \right ) y+4 x^{3} y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.398 |
|
| 13947 |
\begin{align*}
y^{\prime }&=\frac {-x +F \left (x^{2}+y^{2}\right )}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.398 |
|
| 13948 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.398 |
|
| 13949 |
\begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 y x&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.398 |
|
| 13950 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (\frac {1}{2} x +x^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.398 |
|
| 13951 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.400 |
|
| 13952 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.400 |
|
| 13953 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.400 |
|
| 13954 |
\begin{align*}
y^{\prime }&=x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.400 |
|
| 13955 |
\begin{align*}
y y^{\prime \prime }&={\mathrm e}^{x} y \left (\operatorname {a0} +\operatorname {a1} y^{2}\right )+{\mathrm e}^{2 x} \left (\operatorname {a2} +\operatorname {a3} y^{4}\right )+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.401 |
|
| 13956 |
\begin{align*}
1+{y^{\prime }}^{2}&=\frac {\left (x +a \right )^{2}}{2 a x +x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.401 |
|
| 13957 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.401 |
|
| 13958 |
\begin{align*}
a^{2} {y^{\prime \prime }}^{2}-2 a x y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.401 |
|
| 13959 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\left (x^{2}-1\right ) {\mathrm e}^{2 x}+\left (3 x +4\right ) {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.401 |
|
| 13960 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2}+3 x_{3}+4 x_{4} \\
x_{2}^{\prime }&=4 x_{1}+3 x_{2}+2 x_{3}+x_{4} \\
x_{3}^{\prime }&=4 x_{1}+5 x_{2}+6 x_{3}+7 x_{4} \\
x_{4}^{\prime }&=7 x_{1}+6 x_{2}+5 x_{3}+4 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.403 |
|
| 13961 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.404 |
|
| 13962 |
\begin{align*}
{y^{\prime }}^{2}+a y^{\prime }+b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.404 |
|
| 13963 |
\begin{align*}
y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.404 |
|
| 13964 |
\begin{align*}
y^{\prime }&=\frac {1}{-2+y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.404 |
|
| 13965 |
\begin{align*}
y^{\prime \prime }-k^{2} y&=f \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.404 |
|
| 13966 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=4 \sin \left (3 x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.404 |
|
| 13967 |
\begin{align*}
\left (2 y+y^{\prime }\right ) y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.404 |
|
| 13968 |
\begin{align*}
x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.405 |
|
| 13969 |
\begin{align*}
6 x^{2} y^{\prime \prime }+5 x y^{\prime }-y&=0 \\
y \left (1\right ) &= a \\
y^{\prime }\left (1\right ) &= b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.406 |
|
| 13970 |
\begin{align*}
x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.406 |
|
| 13971 |
\begin{align*}
2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y&=\frac {1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.407 |
|
| 13972 |
\begin{align*}
y^{\prime }&=t -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.408 |
|
| 13973 |
\begin{align*}
\left (x y^{\prime }-y\right )^{2}+x^{2} \left (x -y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.408 |
|
| 13974 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.408 |
|
| 13975 |
\begin{align*}
\cos \left (y^{\prime }\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.408 |
|
| 13976 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=2 t^{2}+4 \,{\mathrm e}^{2 t} t +t \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.408 |
|
| 13977 |
\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*} |
✓ |
✓ |
✓ |
✓ |
1.408 |
|
| 13978 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.409 |
|
| 13979 |
\begin{align*}
4 \left (x -4\right )^{2} y^{\prime \prime }+\left (x -4\right ) \left (x -8\right ) y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=4\). |
✓ |
✓ |
✓ |
✓ |
1.409 |
|
| 13980 |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.409 |
|
| 13981 |
\begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )-\operatorname {Heaviside}\left (t -5-k \right ) \left (t -5-k \right )}{k} \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.410 |
|
| 13982 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}+x_{2}+\frac {4}{\sin \left (2 t \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.410 |
|
| 13983 |
\begin{align*}
t^{2} y^{\prime \prime }-3 t y^{\prime }+5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.410 |
|
| 13984 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y-2 \cos \left (x \right )+2 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.410 |
|
| 13985 |
\begin{align*}
y^{\prime }&=\frac {2 \sqrt {-1+y}}{3} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.411 |
|
| 13986 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{6}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.411 |
|
| 13987 |
\begin{align*}
\left (x^{2}+x \right ) y^{\prime \prime }+\left (x -2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.411 |
|
| 13988 |
\begin{align*}
y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y&={\mathrm e}^{x^{2}} \sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.412 |
|
| 13989 |
\begin{align*}
2 x^{\prime }+y^{\prime }-x-y&={\mathrm e}^{-t} \\
x^{\prime }+2 x+y^{\prime }+y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.412 |
|
| 13990 |
\begin{align*}
2 y+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.413 |
|
| 13991 |
\begin{align*}
y^{\prime }&=\left (x +y\right )^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.413 |
|
| 13992 |
\begin{align*}
y^{\prime }-a^{n} f \left (x \right )^{1-n} g^{\prime }\left (x \right ) y^{n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-f \left (x \right ) g^{\prime }\left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.413 |
|
| 13993 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+7 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }-6 x y^{\prime }-6 y&=\cos \left (\ln \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.414 |
|
| 13994 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y&=\tan \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.414 |
|
| 13995 |
\begin{align*}
y^{\prime }&=-\lambda \,{\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\mu x} y-a \,{\mathrm e}^{\left (\mu -\lambda \right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.414 |
|
| 13996 |
\begin{align*}
8 x {y^{\prime }}^{3}&=y \left (12 {y^{\prime }}^{2}-9\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.414 |
|
| 13997 |
\begin{align*}
6 y^{\prime }+6 y^{2}-y-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.415 |
|
| 13998 |
\begin{align*}
y&=x \left (y^{\prime }+1\right )+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.415 |
|
| 13999 |
\begin{align*}
-\left (4 x^{2}+1\right ) y+4 x y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.415 |
|
| 14000 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }&=52 \sin \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.415 |
|