| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 15901 |
\begin{align*}
\left (1-x \right )^{2} y-2 \left (1-x \right )^{2} y^{\prime }+\left (1-x \right )^{2} y^{\prime \prime }&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.431 |
|
| 15902 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=2 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.431 |
|
| 15903 |
\begin{align*}
x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y&=\frac {1}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.431 |
|
| 15904 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.431 |
|
| 15905 |
\begin{align*}
\left (2 x +1\right ) \left (x +1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=\left (2 x +1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.431 |
|
| 15906 |
\begin{align*}
5 x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.433 |
|
| 15907 |
\begin{align*}
y^{\prime }&=-y^{2}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.434 |
|
| 15908 |
\begin{align*}
y^{\prime }-a y&={\mathrm e}^{c t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.434 |
|
| 15909 |
\begin{align*}
y^{\prime \prime }&=\frac {\left (3 \sin \left (x \right )^{2}+1\right ) y^{\prime }}{\cos \left (x \right ) \sin \left (x \right )}+\frac {\sin \left (x \right )^{2} y}{\cos \left (x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.435 |
|
| 15910 |
\begin{align*}
y^{\prime } y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.435 |
|
| 15911 |
\begin{align*}
x \left (y x +1\right ) y^{\prime \prime }+x^{2} {y^{\prime }}^{2}+\left (4 y x +2\right ) y^{\prime }+y^{2}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.435 |
|
| 15912 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.435 |
|
| 15913 |
\begin{align*}
k \left (1+k \right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.436 |
|
| 15914 |
\begin{align*}
-2 y+3 y^{\prime }&={\mathrm e}^{-\frac {\pi t}{2}} \\
y \left (0\right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.436 |
|
| 15915 |
\begin{align*}
y^{\prime \prime }+y&=3 \cos \left (x \right )^{2}+2 \sin \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.436 |
|
| 15916 |
\begin{align*}
y^{\prime }&=3 \left (y+7\right ) x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.437 |
|
| 15917 |
\begin{align*}
y-y^{\prime } x&=3-2 x^{2} y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.437 |
|
| 15918 | \begin{align*}
y^{\prime }-2 y x&={\mathrm e}^{x} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.437 |
|
| 15919 |
\begin{align*}
4 y^{\prime \prime }+24 y^{\prime }+37 y&=17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.437 |
|
| 15920 |
\begin{align*}
y^{\prime \prime }+a^{2} y&=\sec \left (a x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.438 |
|
| 15921 |
\begin{align*}
y^{\prime \prime }&=2 y^{3} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.438 |
|
| 15922 |
\begin{align*}
y^{\prime }-2 y&={\mathrm e}^{x} \left (1-x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.438 |
|
| 15923 |
\begin{align*}
\left (1-x \right ) x^{2} y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.439 |
|
| 15924 |
\begin{align*}
-2 x^{2} y-x^{2} y^{\prime }+x^{2} y^{\prime \prime }&=1+x +2 \ln \left (x \right ) x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.440 |
|
| 15925 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.440 |
|
| 15926 |
\begin{align*}
x^{3}+3 y-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.441 |
|
| 15927 |
\begin{align*}
a \left (a +1\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime }&={\mathrm e}^{x} x^{2+a} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.441 |
|
| 15928 |
\begin{align*}
y y^{\prime \prime }&=y^{\prime } y+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.441 |
|
| 15929 |
\begin{align*}
y^{\prime } y-y&=A \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.441 |
|
| 15930 |
\begin{align*}
y^{\prime }&=t \left (1+y\right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.442 |
|
| 15931 |
\begin{align*}
y-y^{\prime } x&=3-2 x^{2} y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.442 |
|
| 15932 |
\begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.442 |
|
| 15933 |
\begin{align*}
25 x^{2} y^{\prime \prime }+\left (4+2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.442 |
|
| 15934 |
\begin{align*}
y^{\prime }&=1+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.443 |
|
| 15935 |
\begin{align*}
x^{\prime }+x&=a t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.444 |
|
| 15936 |
\begin{align*}
y^{\prime }+2 y&=\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.444 |
|
| 15937 | \begin{align*}
y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.444 |
|
| 15938 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.446 |
|
| 15939 |
\begin{align*}
\left (x^{2}+y^{2}+x \right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.446 |
|
| 15940 |
\begin{align*}
2 \left (1-x \right )^{2} x^{2} \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime }&=\operatorname {a0} x \left (1-y\right )^{2} \left (x -y\right )^{2}+\left (-1+\operatorname {a2} \right ) \left (1-x \right ) x \left (1-y\right )^{2} y^{2}+\operatorname {a1} \left (1-x \right ) \left (x -y\right )^{2} y^{2}+\operatorname {a3} \left (1-y\right )^{2} \left (x -y\right )^{2} y^{2}+2 \left (1-x \right ) x \left (1-y\right )^{2} y \left (x^{2}+y-2 y x \right ) y^{\prime }+\left (1-x \right )^{2} x^{2} \left (x -2 y-2 y x +3 y^{2}\right ) {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.446 |
|
| 15941 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.446 |
|
| 15942 |
\begin{align*}
y^{\prime }&=\frac {2 x \left (y-1\right )}{x^{2}+3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.447 |
|
| 15943 |
\begin{align*}
y^{\prime }&=x \left (x^{3}+2\right )-\left (2 x^{2}-y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.447 |
|
| 15944 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=6 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.447 |
|
| 15945 |
\begin{align*}
y x +x +2 y+1+\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.448 |
|
| 15946 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}+8 x_{2}+9 t \\
x_{2}^{\prime }&=x_{1}+x_{2}+3 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.448 |
|
| 15947 |
\begin{align*}
y^{\prime } y&=a_{0} +a_{1} y+a_{2} y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.448 |
|
| 15948 |
\begin{align*}
y^{\prime }-5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.448 |
|
| 15949 |
\begin{align*}
y^{\prime } \left (x -\ln \left (y^{\prime }\right )\right )&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.449 |
|
| 15950 |
\begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.449 |
|
| 15951 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.449 |
|
| 15952 |
\begin{align*}
y^{\prime }+\frac {y \ln \left (x \right )}{x}&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.449 |
|
| 15953 |
\begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }-\left (x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
1.449 |
|
| 15954 |
\begin{align*}
y^{\prime }&=1+x +y+y x \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.450 |
|
| 15955 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.450 |
|
| 15956 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.451 |
|
| 15957 | \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=2 x^{3} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.451 |
|
| 15958 |
\begin{align*}
y^{\prime }&=x \,{\mathrm e}^{y^{2}-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.451 |
|
| 15959 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=0 \\
y \left (1\right ) &= -1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.451 |
|
| 15960 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
1.451 |
|
| 15961 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.452 |
|
| 15962 |
\begin{align*}
x^{\prime }-x^{3}&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.452 |
|
| 15963 |
\begin{align*}
y^{\prime }-2 y x&=-1 \\
y \left (0\right ) &= \frac {\sqrt {\pi }}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.452 |
|
| 15964 |
\begin{align*}
x^{\prime }&=x+2 y+\sin \left (t \right ) \\
y^{\prime }&=-x+y-\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.452 |
|
| 15965 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.452 |
|
| 15966 |
\begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.452 |
|
| 15967 |
\begin{align*}
y^{\prime } x +y&=2 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.454 |
|
| 15968 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.454 |
|
| 15969 |
\begin{align*}
x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y&=\frac {1}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.454 |
|
| 15970 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.454 |
|
| 15971 |
\begin{align*}
y^{\prime }+2 x y \left (1-a \,x^{2} y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.455 |
|
| 15972 |
\begin{align*}
\frac {2 x y^{\prime } y}{3}&=\sqrt {x^{6}-y^{4}}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.455 |
|
| 15973 |
\begin{align*}
\left (4 y^{3}-a y-b \right ) \left (y^{\prime \prime }+f y^{\prime }\right )-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.455 |
|
| 15974 |
\begin{align*}
x_{1}^{\prime }&=-5 x_{1}-2 x_{2}-x_{3}+2 x_{4}+3 x_{5} \\
x_{2}^{\prime }&=-3 x_{2} \\
x_{3}^{\prime }&=x_{1}-x_{3}-x_{5} \\
x_{4}^{\prime }&=2 x_{1}+x_{2}-4 x_{4}-2 x_{5} \\
x_{5}^{\prime }&=-3 x_{1}-2 x_{2}-x_{3}+2 x_{4}+x_{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.455 |
|
| 15975 |
\begin{align*}
y^{2} {y^{\prime }}^{3}-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.455 |
|
| 15976 | \begin{align*}
y^{\prime }&={\mathrm e}^{2 y+3 x} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.455 |
|
| 15977 |
\begin{align*}
y^{\prime }+y&=\left (x +1\right )^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.456 |
|
| 15978 |
\begin{align*}
x {y^{\prime }}^{2}-y^{\prime } y-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.456 |
|
| 15979 |
\begin{align*}
y^{\prime \prime } x -3 y^{\prime }+\frac {3 y}{x}&=2+x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.456 |
|
| 15980 |
\begin{align*}
y^{\prime }&=x^{2}+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.456 |
|
| 15981 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.457 |
|
| 15982 |
\begin{align*}
4 \left (x^{2}+1\right ) y^{\prime }-4 y x -x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.457 |
|
| 15983 |
\begin{align*}
\left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+\left (2 a x +c \right ) \left (a \,x^{2}+b \right ) y^{\prime }+k y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.457 |
|
| 15984 |
\begin{align*}
1+\left (1-x \tan \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.457 |
|
| 15985 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=9 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.458 |
|
| 15986 |
\begin{align*}
y^{\prime }&=-4 y+3 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.458 |
|
| 15987 |
\begin{align*}
x^{2} y^{\prime }+y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.458 |
|
| 15988 |
\begin{align*}
y^{\prime } x&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.460 |
|
| 15989 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{1-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.460 |
|
| 15990 |
\begin{align*}
{y^{\prime }}^{3}+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.460 |
|
| 15991 |
\begin{align*}
\left (y^{2}-x \right ) y^{\prime }-y+x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.461 |
|
| 15992 |
\begin{align*}
y^{\prime }+y^{2}&=x^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.461 |
|
| 15993 |
\begin{align*}
2 y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.461 |
|
| 15994 |
\begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }-\left (t +1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.462 |
|
| 15995 | \begin{align*}
y^{\prime \prime }-y x -x^{3}&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.462 |
|
| 15996 |
\begin{align*}
y^{\prime }-f \left (x \right ) y^{n}-g \left (x \right ) y-h \left (x \right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.462 |
|
| 15997 |
\begin{align*}
\left (x +a \right ) y^{\prime \prime }+\left (b x +c \right ) y^{\prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.462 |
|
| 15998 |
\begin{align*}
x^{\prime }+x \tanh \left (t \right )&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.462 |
|
| 15999 |
\begin{align*}
-y^{\prime }+y^{\prime \prime } x&=3 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.462 |
|
| 16000 |
\begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=2 x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.463 |
|