| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 15901 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| 15902 |
\begin{align*}
x^{\prime }-y^{\prime }-2 x+4 y&=t \\
x^{\prime }+y^{\prime }-x-y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.218 |
|
| 15903 |
\begin{align*}
u^{\prime }&=\alpha \left (1-u\right )-\beta u \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.219 |
|
| 15904 |
\begin{align*}
y^{\prime }&=\left (x +y\right )^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.219 |
|
| 15905 |
\begin{align*}
y^{\prime \prime }&=x^{2} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.219 |
|
| 15906 |
\begin{align*}
y^{\prime }&=y \left (3-t y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.220 |
|
| 15907 |
\begin{align*}
\left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.221 |
|
| 15908 |
\begin{align*}
y^{\left (6\right )}+2 y^{\left (5\right )}+5 y^{\prime \prime \prime \prime }&=x^{3}+x^{2} {\mathrm e}^{-x}+{\mathrm e}^{-x} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.221 |
|
| 15909 |
\begin{align*}
y^{\prime }&=x \,{\mathrm e}^{-x^{2}+y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.221 |
|
| 15910 |
\begin{align*}
y^{\prime }&=\frac {y}{x -1}+x^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.221 |
|
| 15911 |
\begin{align*}
\frac {4 x^{3}}{y^{2}}+\frac {3}{y}+\left (\frac {3 x}{y^{2}}+4 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.222 |
|
| 15912 |
\begin{align*}
3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=5 {y^{\prime \prime \prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.222 |
|
| 15913 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.222 |
|
| 15914 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=1-\operatorname {Heaviside}\left (t -\pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.223 |
|
| 15915 |
\begin{align*}
{y^{\prime }}^{2}-y y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.223 |
|
| 15916 |
\begin{align*}
y^{\prime }&=-x \,{\mathrm e}^{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.224 |
|
| 15917 |
\begin{align*}
1&=\left (x +y^{2}\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.224 |
|
| 15918 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\
y \left (\pi \right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 2 \,{\mathrm e}^{-\pi }-2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.224 |
|
| 15919 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}-\ln \left (y\right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.224 |
|
| 15920 |
\begin{align*}
y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.224 |
|
| 15921 |
\begin{align*}
y y^{\prime \prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3}+\operatorname {a4} y^{4}+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.225 |
|
| 15922 |
\begin{align*}
y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.225 |
|
| 15923 |
\begin{align*}
y^{\prime \prime }-\frac {a f^{\prime }\left (x \right ) y^{\prime }}{f \left (x \right )}+b f \left (x \right )^{2 a} y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.225 |
|
| 15924 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.225 |
|
| 15925 |
\begin{align*}
y^{\prime }&=a \left (t \right ) y+q \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.225 |
|
| 15926 |
\begin{align*}
y^{\prime }&=x -2 y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.225 |
|
| 15927 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x} y \\
y \left (0\right ) &= 2 \,{\mathrm e} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.226 |
|
| 15928 |
\begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.226 |
|
| 15929 |
\begin{align*}
t^{2} y^{\prime \prime }+2 y^{\prime } t +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| 15930 |
\begin{align*}
y^{\prime }&=2 x -y \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| 15931 |
\begin{align*}
y^{\prime } x -4 y&=x^{6} {\mathrm e}^{x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.228 |
|
| 15932 |
\begin{align*}
y^{\left (6\right )}-y&=x^{10} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.229 |
|
| 15933 |
\begin{align*}
t y+y^{\prime }&=1+t \\
y \left (\frac {3}{2}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.230 |
|
| 15934 |
\begin{align*}
a \left (1+a \right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime }&={\mathrm e}^{x} x^{2+a} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.230 |
|
| 15935 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.230 |
|
| 15936 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x} y \\
y \left (0\right ) &= 2 \,{\mathrm e} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| 15937 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (9 x^{2}-4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| 15938 |
\begin{align*}
y^{\prime }&=-\frac {y}{t}+\cos \left (t^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| 15939 |
\begin{align*}
y^{\prime }&=1-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.232 |
|
| 15940 |
\begin{align*}
x^{\prime }&=\left (x-1\right ) \left (1-2 x\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.232 |
|
| 15941 |
\begin{align*}
y y^{\prime \prime }+2 y^{\prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.233 |
|
| 15942 |
\begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.233 |
|
| 15943 |
\begin{align*}
y^{\prime }&=y^{2}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.235 |
|
| 15944 |
\begin{align*}
-\frac {3 y}{2}+y^{\prime }&=2 \,{\mathrm e}^{t}+3 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.236 |
|
| 15945 |
\begin{align*}
y^{\prime \prime }-36 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.236 |
|
| 15946 |
\begin{align*}
y^{\prime }&=y \sin \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.236 |
|
| 15947 |
\begin{align*}
y-y^{\prime } x +\left (-x \cot \left (x \right )+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.236 |
|
| 15948 |
\begin{align*}
\frac {\left (x +y-a \right ) y^{\prime }}{x +y-b}&=\frac {x +y+a}{x +y+b} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.236 |
|
| 15949 |
\begin{align*}
\frac {y}{4}+y^{\prime }&=3+2 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.237 |
|
| 15950 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.237 |
|
| 15951 |
\begin{align*}
y^{\prime }+y&=x^{2}+2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.238 |
|
| 15952 |
\begin{align*}
y^{\prime }&=y-\cos \left (\frac {\pi x}{2}\right ) \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.238 |
|
| 15953 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+\left (x -\frac {4}{x}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.238 |
|
| 15954 |
\begin{align*}
y y^{\prime }-x y^{2}+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.239 |
|
| 15955 |
\begin{align*}
y^{\prime \prime }&=a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.240 |
|
| 15956 |
\begin{align*}
x^{6} {y^{\prime }}^{2}&=8 y^{\prime } x +16 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.240 |
|
| 15957 |
\begin{align*}
y^{\prime \prime }-4 y&=12 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.241 |
|
| 15958 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+x^{m} b +c \right ) y^{\prime }+\left (c -1\right ) \left (a \,x^{n -1}+x^{m -1} b \right ) y&=0 \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
2.241 |
|
| 15959 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.242 |
|
| 15960 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left ({\mathrm e}^{\frac {2}{x}}-v^{2}\right ) y}{x^{4}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.242 |
|
| 15961 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-n^{2}+x^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.242 |
|
| 15962 |
\begin{align*}
y^{2} x^{2}+1+2 x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.242 |
|
| 15963 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime }+3 y x&=x \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.243 |
|
| 15964 |
\begin{align*}
-y+y^{\prime } t&=t^{3} {\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.243 |
|
| 15965 |
\begin{align*}
2 t^{2} y^{\prime \prime }-5 y^{\prime } t +3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.243 |
|
| 15966 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.244 |
|
| 15967 |
\begin{align*}
y^{\prime }&=2 y \left (5-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.244 |
|
| 15968 |
\begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.245 |
|
| 15969 |
\begin{align*}
y^{\prime } x -2 y&=-x^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.246 |
|
| 15970 |
\begin{align*}
y^{\prime }&=\frac {2 a}{y+2 F \left (y^{2}-4 a x \right ) a} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.246 |
|
| 15971 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }-y x&=2 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.246 |
|
| 15972 |
\begin{align*}
x^{\prime }&=t x-t^{3} \\
x \left (a \right ) &= a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.247 |
|
| 15973 |
\begin{align*}
3 y+x^{3} y^{4}+3 y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.248 |
|
| 15974 |
\begin{align*}
y^{\prime \prime }+k^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.250 |
|
| 15975 |
\begin{align*}
y^{\prime \prime }&=-3 y \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.250 |
|
| 15976 |
\begin{align*}
3 y^{\prime \prime } x -\left (x -2\right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.250 |
|
| 15977 |
\begin{align*}
y^{\prime }&=y^{{2}/{3}}+a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.250 |
|
| 15978 |
\begin{align*}
y^{\prime }&=\frac {3 x^{2}+1}{-6 y+3 y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.251 |
|
| 15979 |
\begin{align*}
y^{\prime \prime } x -y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.253 |
|
| 15980 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.253 |
|
| 15981 |
\begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.253 |
|
| 15982 |
\begin{align*}
y&=y^{\prime } x +a \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.253 |
|
| 15983 |
\begin{align*}
y^{\prime }&=-\frac {1}{2 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.253 |
|
| 15984 |
\begin{align*}
i^{\prime }-6 i&=10 \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.254 |
|
| 15985 |
\begin{align*}
y^{\prime }&=y x +\frac {1}{x^{2}+1} \\
y \left (-5\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.254 |
|
| 15986 |
\begin{align*}
t x^{\prime }+x&=2 t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.254 |
|
| 15987 |
\begin{align*}
y^{\prime \prime }+p \left (x \right ) y^{\prime }+q \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.255 |
|
| 15988 |
\begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=0 \\
y \left (1\right ) &= -3 \\
y^{\prime }\left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.255 |
|
| 15989 |
\begin{align*}
y^{\prime }+y&=x y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.256 |
|
| 15990 |
\begin{align*}
\left (x +1\right ) y^{\prime }+y&=\ln \left (x \right ) \\
y \left (1\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.256 |
|
| 15991 |
\begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.257 |
|
| 15992 |
\begin{align*}
y-y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.257 |
|
| 15993 |
\begin{align*}
y^{\prime }&=y+\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.257 |
|
| 15994 |
\begin{align*}
x^{2} y^{\prime }+x \left (2+x \right ) y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.258 |
|
| 15995 |
\begin{align*}
y^{\prime }&=\frac {2 x}{y+x^{2} y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.259 |
|
| 15996 |
\begin{align*}
y^{\prime }+x +\cot \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.259 |
|
| 15997 |
\begin{align*}
2 y y^{\prime \prime }&=y^{2} \left (a +b y\right )+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.259 |
|
| 15998 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.259 |
|
| 15999 |
\begin{align*}
y^{\prime }&=\frac {y}{x \left (-1+F \left (y x \right ) y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.259 |
|
| 16000 |
\begin{align*}
x^{\prime }&=2 x+\operatorname {Heaviside}\left (t -1\right ) \\
x \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
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