| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 20001 |
\begin{align*}
\sin \left (y\right )-2 x \cos \left (y\right )^{2}+x \cos \left (y\right ) \left (2 \sin \left (y\right ) x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.329 |
|
| 20002 |
\begin{align*}
\left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.330 |
|
| 20003 |
\begin{align*}
1+y+\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.332 |
|
| 20004 |
\begin{align*}
y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\
y \left (1\right ) &= -{\frac {1}{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.333 |
|
| 20005 |
\begin{align*}
y-x y^{\prime }+\left (-x \cot \left (x \right )+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.333 |
|
| 20006 |
\begin{align*}
y \left (y+1\right ) y^{\prime }&=x \left (x +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.334 |
|
| 20007 |
\begin{align*}
x +x y^{2}+{\mathrm e}^{x^{2}} y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.334 |
|
| 20008 |
\begin{align*}
y^{\prime }&=2 \csc \left (2 x \right ) \left (\sin \left (x \right )^{3}+y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.335 |
|
| 20009 |
\begin{align*}
y y^{\prime }-x y^{2}+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.335 |
|
| 20010 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.336 |
|
| 20011 |
\begin{align*}
y^{\prime }&=\frac {a^{2} x +a^{3} x^{3}+a^{3} x^{3} y^{2}+2 a^{2} x^{2} y+a x +a^{3} x^{3} y^{3}+3 y^{2} a^{2} x^{2}+3 a x y+1}{a^{3} x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.336 |
|
| 20012 |
\begin{align*}
\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.339 |
|
| 20013 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.340 |
|
| 20014 |
\begin{align*}
\left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+b^{2}+x^{2}+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.343 |
|
| 20015 |
\begin{align*}
y^{\prime }&=y-y^{3} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
4.344 |
|
| 20016 |
\begin{align*}
\left (t^{2}+1\right ) y^{\prime }&=1+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.345 |
|
| 20017 |
\begin{align*}
y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\
y \left (1\right ) &= -{\frac {1}{5}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.345 |
|
| 20018 |
\begin{align*}
y^{\prime \prime }&=\operatorname {f4} \left (x \right )+\operatorname {f3} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\left (\operatorname {f1} \left (x \right )-2 y\right ) y^{\prime } \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
4.346 |
|
| 20019 |
\begin{align*}
x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.346 |
|
| 20020 |
\begin{align*}
y^{\prime }&=\frac {-x +1-2 y+3 x^{2}-2 x^{2} y+2 x^{4}+x^{3}-2 x^{3} y+2 x^{5}}{x^{2}-y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.346 |
|
| 20021 |
\begin{align*}
y^{\prime }&=\frac {x y^{2}}{\sqrt {x^{2}+1}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.348 |
|
| 20022 |
\begin{align*}
\left (a \,x^{n}+b \right )^{m +1} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }-a n m \,x^{n -1} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.351 |
|
| 20023 |
\begin{align*}
y^{\prime }&=f \left (x \right )+x f \left (x \right ) y+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.352 |
|
| 20024 |
\begin{align*}
\cos \left (x +y^{2}\right )+3 y+\left (2 y \cos \left (x +y^{2}\right )+3 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.355 |
|
| 20025 |
\begin{align*}
x y^{\prime }+2 y&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.356 |
|
| 20026 |
\begin{align*}
x^{7} y^{2} {y^{\prime }}^{3}-\left (3 x^{6} y^{3}-1\right ) {y^{\prime }}^{2}+3 x^{5} y^{4} y^{\prime }-x^{4} y^{5}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.356 |
|
| 20027 |
\begin{align*}
y^{\prime }-y x&=-x^{2}+1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.356 |
|
| 20028 |
\begin{align*}
y^{\prime }+\frac {y}{x -2}&=3 x \\
y \left (3\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.356 |
|
| 20029 |
\begin{align*}
y^{\prime } \left (x^{2}+2\right )&=4 x \left (y^{2}+2 y+1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.357 |
|
| 20030 |
\begin{align*}
\left (x^{2}+2 y+y^{2}\right ) y^{\prime }+2 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.357 |
|
| 20031 |
\begin{align*}
x^{2}+y+y^{2}-x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.358 |
|
| 20032 |
\begin{align*}
y^{\prime }+\frac {2 y}{x}&=\frac {3 y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.358 |
|
| 20033 |
\begin{align*}
y^{\prime }-\operatorname {R1} \left (x , \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}\right ) \operatorname {R2} \left (y, \sqrt {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.359 |
|
| 20034 |
\begin{align*}
y^{\prime \prime }+9 y&=9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.359 |
|
| 20035 |
\begin{align*}
y^{\prime }&=\frac {32 x^{5}+64 x^{6}+64 x^{6} y^{2}+32 x^{4} y+4 x^{2}+64 x^{6} y^{3}+48 y^{2} x^{4}+12 x^{2} y+1}{64 x^{8}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.360 |
|
| 20036 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+\frac {5 y}{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.361 |
|
| 20037 |
\begin{align*}
x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right )&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
4.361 |
|
| 20038 |
\begin{align*}
9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.363 |
|
| 20039 |
\begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 4 t & 0\le t \le 1 \\ 4 & 1<t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.364 |
|
| 20040 |
\begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
4.365 |
|
| 20041 |
\begin{align*}
y&=x y^{\prime }+\frac {1}{y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.367 |
|
| 20042 |
\begin{align*}
y^{\prime \prime }&=a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.369 |
|
| 20043 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.370 |
|
| 20044 |
\begin{align*}
2+3 x^{2}-2 y x +\left (3-x^{2}+6 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.371 |
|
| 20045 |
\begin{align*}
y^{\prime }+2 y x&=0 \\
y \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.372 |
|
| 20046 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.372 |
|
| 20047 |
\begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.372 |
|
| 20048 |
\begin{align*}
y^{\prime }&=\frac {\left (-256 a \,x^{2}+512+512 y^{2}+128 y a \,x^{4}+8 a^{2} x^{8}+512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.374 |
|
| 20049 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=x^{2} y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.374 |
|
| 20050 |
\begin{align*}
y^{\prime }&=-\frac {y^{2}}{x}+\frac {2 y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.374 |
|
| 20051 |
\begin{align*}
x^{\prime }&=\sin \left (x t \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
4.378 |
|
| 20052 |
\begin{align*}
y^{\prime }&=\sec \left (x \right )^{2} \cot \left (y\right ) \cos \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.379 |
|
| 20053 |
\begin{align*}
x y^{\prime }&=a y^{2}+b y+c \,x^{2 b} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.380 |
|
| 20054 |
\begin{align*}
x^{\prime \prime }+9 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.380 |
|
| 20055 |
\begin{align*}
x \left (x +1\right ) y^{\prime }&=\left (1-2 x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.385 |
|
| 20056 |
\begin{align*}
y-x y^{\prime }+\ln \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.385 |
|
| 20057 |
\begin{align*}
y^{\prime }&=x \,{\mathrm e}^{y^{2}-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.387 |
|
| 20058 |
\begin{align*}
x y^{\prime }+2 y&=3 x \\
y \left (1\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.388 |
|
| 20059 |
\begin{align*}
t -y+t y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.389 |
|
| 20060 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{t} \cos \left (2 t \right )+{\mathrm e}^{2 t} \left (3 t +4\right ) \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.389 |
|
| 20061 |
\begin{align*}
y^{\prime }&=\frac {3 y}{x +1}-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.390 |
|
| 20062 |
\begin{align*}
y^{\prime }&=\frac {1}{2 x -y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.392 |
|
| 20063 |
\begin{align*}
m v^{\prime }&=m g -k v^{2} \\
v \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.395 |
|
| 20064 |
\begin{align*}
b \tan \left (x \right )^{2} y-2 \csc \left (2 x \right ) \left (1-a \sin \left (x \right )^{2}\right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.395 |
|
| 20065 |
\begin{align*}
y^{\prime }&=\sqrt {1+6 x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.395 |
|
| 20066 |
\begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }+6 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.395 |
|
| 20067 |
\begin{align*}
\cos \left (x \right ) y^{\prime }-y \sin \left (x \right )&=2 x \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.395 |
|
| 20068 |
\begin{align*}
x^{2} y^{3}+y+\left (x^{3} y^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.395 |
|
| 20069 |
\begin{align*}
x y^{\prime }+y^{2}+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.396 |
|
| 20070 |
\begin{align*}
y^{\prime }&=y \cot \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.397 |
|
| 20071 |
\begin{align*}
y^{\prime \prime }-a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.397 |
|
| 20072 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.397 |
|
| 20073 |
\begin{align*}
x y^{\prime }+b x +\left (2+a x y\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.398 |
|
| 20074 |
\begin{align*}
x y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.398 |
|
| 20075 |
\begin{align*}
y^{\prime }&=\frac {y+1}{x -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.398 |
|
| 20076 |
\begin{align*}
y^{\prime }+y^{2}+\frac {y}{x}-\frac {4}{x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.398 |
|
| 20077 |
\begin{align*}
y^{\prime }&=x^{3} \left (-x +y\right )^{2}+\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.400 |
|
| 20078 |
\begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.401 |
|
| 20079 |
\begin{align*}
y^{\prime }&=x \,{\mathrm e}^{y-x^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.401 |
|
| 20080 |
\begin{align*}
-y+t y^{\prime }&=t^{3} {\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.401 |
|
| 20081 |
\begin{align*}
x y^{\prime \prime }-y^{\prime }-4 x^{3} y&=8 x^{3} \sin \left (x^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.401 |
|
| 20082 |
\begin{align*}
y^{\prime }&=\frac {y+x^{3} a \,{\mathrm e}^{x}+a \,x^{4}+a \,x^{3}-x y^{2} {\mathrm e}^{x}-x^{2} y^{2}-x y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.402 |
|
| 20083 |
\begin{align*}
\frac {2 y^{3}-2 x^{2} y^{3}-x +x y^{2} \ln \left (y\right )}{x y^{2}}+\frac {\left (2 y^{3} \ln \left (x \right )-x^{2} y^{3}+2 x +x y^{2}\right ) y^{\prime }}{y^{3}}&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.404 |
|
| 20084 |
\begin{align*}
2 y y^{\prime }&=x y^{2}+x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.404 |
|
| 20085 |
\begin{align*}
x^{\prime }&=\sin \left (x\right )^{2} \cos \left (t \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.404 |
|
| 20086 |
\begin{align*}
y^{\prime }&=x^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.405 |
|
| 20087 |
\begin{align*}
x y^{\prime }+\left (1+3 x \right ) y&={\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.406 |
|
| 20088 |
\begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.407 |
|
| 20089 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.407 |
|
| 20090 |
\begin{align*}
y^{\prime }&={\mathrm e}^{t +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.407 |
|
| 20091 |
\begin{align*}
y^{\prime }&=y \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.408 |
|
| 20092 |
\begin{align*}
y^{\prime }&=y \,{\mathrm e}^{-x^{2}} \\
y \left (4\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.408 |
|
| 20093 |
\begin{align*}
y^{\prime }&=-y t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.408 |
|
| 20094 |
\begin{align*}
\sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.409 |
|
| 20095 |
\begin{align*}
-y+2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
4.409 |
|
| 20096 |
\begin{align*}
\sqrt {a^{2}-x^{2}}\, \left (-y y^{\prime }-{y^{\prime }}^{2} x +x y y^{\prime \prime }\right )&=b x {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
4.409 |
|
| 20097 |
\begin{align*}
y^{\prime }-3 x^{2} y^{2}&=-3 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.412 |
|
| 20098 |
\begin{align*}
y^{\prime }&=\cot \left (x \right ) \cot \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.414 |
|
| 20099 |
\begin{align*}
y+y^{\prime }&=\frac {{\mathrm e}^{t}}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.414 |
|
| 20100 |
\begin{align*}
x y^{\prime }+y&=x \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.415 |
|