| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 16001 |
\begin{align*}
y^{\prime } x&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.463 |
|
| 16002 |
\begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
y \left (\pi \right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.463 |
|
| 16003 |
\begin{align*}
y^{\prime }+y x&=x^{3} y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.464 |
|
| 16004 |
\begin{align*}
y^{\prime \prime }-y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.464 |
|
| 16005 |
\begin{align*}
y^{\prime }+2 x y \left (1+a \,x^{2} y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.465 |
|
| 16006 |
\begin{align*}
y^{\prime }&=a +b \cos \left (A x +B y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.465 |
|
| 16007 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=a x \\
y \left (0\right ) &= 2 a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.466 |
|
| 16008 |
\begin{align*}
y^{\prime } y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.466 |
|
| 16009 |
\begin{align*}
x \left (1-2 x \right ) y^{\prime }+1+\left (1-4 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.467 |
|
| 16010 |
\begin{align*}
y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.467 |
|
| 16011 |
\begin{align*}
y^{\prime \prime }+y-\sin \left (a x \right ) \sin \left (b x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.467 |
|
| 16012 |
\begin{align*}
y^{\prime \prime }+\left (a b \,x^{n}+b \,x^{n -1}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{n}+1\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.467 |
|
| 16013 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }-b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.467 |
|
| 16014 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }&=-{\mathrm e}^{3 t}-2 t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {8}{9}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.467 |
|
| 16015 |
\begin{align*}
3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z&=0 \\
z \left (1\right ) &= 2 \\
z^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.468 |
|
| 16016 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.468 |
|
| 16017 |
\begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.469 |
|
| 16018 | \begin{align*}
y^{\prime \prime }+2 a x y^{\prime }+y a^{2} x^{2}&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 1.469 |
|
| 16019 |
\begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.470 |
|
| 16020 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x -y&=0 \\
y \left (4\right ) &= 0 \\
y^{\prime }\left (4\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.470 |
|
| 16021 |
\begin{align*}
\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
1.470 |
|
| 16022 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=\sqrt {x}+\frac {1}{\sqrt {x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.470 |
|
| 16023 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.471 |
|
| 16024 |
\begin{align*}
y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+18 y^{\prime \prime }+30 y^{\prime }+25 y&={\mathrm e}^{-t} \cos \left (2 t \right )+{\mathrm e}^{-2 t} \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.471 |
|
| 16025 |
\begin{align*}
y+2 y^{\prime }&=3 t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.471 |
|
| 16026 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {n \left (n +1\right ) y}{x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.471 |
|
| 16027 |
\begin{align*}
y^{\prime }&=1+\left (t -y\right )^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.471 |
|
| 16028 |
\begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{n} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.472 |
|
| 16029 |
\begin{align*}
\sqrt {y}\, y^{\prime \prime }-a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.472 |
|
| 16030 |
\begin{align*}
y^{\prime }&={\mathrm e}^{y} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.473 |
|
| 16031 |
\begin{align*}
y^{\prime } x&=a x -\left (-b \,x^{2}+1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.473 |
|
| 16032 |
\begin{align*}
y^{\prime }&=1+y \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.473 |
|
| 16033 |
\begin{align*}
{y^{\prime }}^{2}-2 y^{\prime }-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.473 |
|
| 16034 |
\begin{align*}
x^{2}+y+\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.473 |
|
| 16035 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.473 |
|
| 16036 |
\begin{align*}
2 y y^{\prime }&=y^{2}+t -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.473 |
|
| 16037 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=6 \ln \left (x \right ) x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| 16038 | \begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+g^{\prime }\left (x \right ) y+a f \left (x \right ) {\mathrm e}^{2 g \left (x \right )} \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 1.474 |
|
| 16039 |
\begin{align*}
x^{\prime }&=2 t x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| 16040 |
\begin{align*}
y^{\prime }&=y^{2}-6 y-16 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| 16041 |
\begin{align*}
\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| 16042 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }&=\left (y-1\right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| 16043 |
\begin{align*}
4 y y^{\prime \prime }&=a y+b y^{2}+c y^{3}+3 {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.475 |
|
| 16044 |
\begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.475 |
|
| 16045 |
\begin{align*}
\left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.475 |
|
| 16046 |
\begin{align*}
x^{\prime }&=\sin \left (t x\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.476 |
|
| 16047 |
\begin{align*}
\left (1-\frac {1}{x}\right ) u^{\prime \prime }+\left (\frac {2}{x}-\frac {2}{x^{2}}-\frac {1}{x^{3}}\right ) u^{\prime }-\frac {u}{x^{4}}&=\frac {2}{x}-\frac {2}{x^{2}}-\frac {2}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.476 |
|
| 16048 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.476 |
|
| 16049 |
\begin{align*}
y^{\prime }+y^{2}&=x^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.477 |
|
| 16050 |
\begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }+2 \left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| 16051 |
\begin{align*}
x^{\prime }&=x+2 y-4 t +1 \\
y^{\prime }&=-x+2 y+3 t +4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| 16052 |
\begin{align*}
-\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.477 |
|
| 16053 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=\frac {5}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| 16054 |
\begin{align*}
9 y^{\prime \prime }+49 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| 16055 |
\begin{align*}
\left (t +1\right ) y^{\prime }+y&=0 \\
y \left (1\right ) &= -9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| 16056 |
\begin{align*}
L q^{\prime \prime }+R q^{\prime }+\frac {q}{c}&=E_{0} \sin \left (\omega t \right ) \\
q \left (0\right ) &= 0 \\
q^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.479 |
|
| 16057 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }-3 y^{\prime } x +\left (3-2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.479 |
|
| 16058 | \begin{align*}
y-x^{3}+\left (y^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 1.480 |
|
| 16059 |
\begin{align*}
2 y y^{\prime \prime }&=4 y^{2}+3 {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.480 |
|
| 16060 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=5 x +4 \,{\mathrm e}^{x} \left (1+\sin \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.480 |
|
| 16061 |
\begin{align*}
y^{\prime \prime }+\left (a \cos \left (2 x \right )+b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.480 |
|
| 16062 |
\begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.480 |
|
| 16063 |
\begin{align*}
y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.481 |
|
| 16064 |
\begin{align*}
y-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.481 |
|
| 16065 |
\begin{align*}
2 y+y^{\prime }&=1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.481 |
|
| 16066 |
\begin{align*}
y^{\prime \prime }+100 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.481 |
|
| 16067 |
\begin{align*}
y^{\prime }&=y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.482 |
|
| 16068 |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.483 |
|
| 16069 |
\begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.483 |
|
| 16070 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.484 |
|
| 16071 |
\begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.484 |
|
| 16072 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\
y \left (1\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.484 |
|
| 16073 |
\begin{align*}
y x -1+\left (x^{2}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.485 |
|
| 16074 |
\begin{align*}
y^{\prime }+4 y&={\mathrm e}^{-4 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.485 |
|
| 16075 |
\begin{align*}
x^{2}&=a^{2} \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.485 |
|
| 16076 |
\begin{align*}
a y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.485 |
|
| 16077 | \begin{align*}
3 y^{\prime }+y x&={\mathrm e}^{-x^{2}} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.485 |
|
| 16078 |
\begin{align*}
x \left (1-x \right ) y^{\prime }+2-3 y x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.486 |
|
| 16079 |
\begin{align*}
x^{\prime }&=2 x+5 y \\
y^{\prime }&=-2 x+\cos \left (3 t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.486 |
|
| 16080 |
\begin{align*}
x^{2}-2 y+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.486 |
|
| 16081 |
\begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.486 |
|
| 16082 |
\begin{align*}
y^{\prime \prime } x +\left (-x^{3}+x \right ) y^{\prime }+y \sin \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.487 |
|
| 16083 |
\begin{align*}
\ln \left (x \right ) y^{\prime }+\frac {x +y}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.487 |
|
| 16084 |
\begin{align*}
2 x y^{\prime } y+a +y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.487 |
|
| 16085 |
\begin{align*}
2 y+y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.487 |
|
| 16086 |
\begin{align*}
y^{\prime }&=y+\frac {1}{1-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.487 |
|
| 16087 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.488 |
|
| 16088 |
\begin{align*}
\left (x^{2}-2\right ) y^{\prime \prime }+2 y^{\prime }+y \sin \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.489 |
|
| 16089 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.489 |
|
| 16090 |
\begin{align*}
y^{2} \left (y^{\prime }-1\right )&=\left (2-y^{\prime }\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.489 |
|
| 16091 |
\begin{align*}
y^{\prime \prime }-8 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.490 |
|
| 16092 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\left \{\begin {array}{cc} \sin \left (2 t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.491 |
|
| 16093 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{5}+y \\
y \left (2\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.491 |
|
| 16094 |
\begin{align*}
y^{\prime }&=x^{2}+2 x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.491 |
|
| 16095 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=24 x +24 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.491 |
|
| 16096 | \begin{align*}
y^{\prime \prime }+y^{\prime }+4 y&=t^{2}+\left (2 t +3\right ) \left (1+\cos \left (t \right )\right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.492 |
|
| 16097 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.492 |
|
| 16098 |
\begin{align*}
x^{\prime }&=2 x+6 y-2 z+50 \,{\mathrm e}^{t} \\
y^{\prime }&=6 x+2 y-2 z+21 \,{\mathrm e}^{-t} \\
z^{\prime }&=-x+6 y+z+9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.493 |
|
| 16099 |
\begin{align*}
h^{2}+\frac {2 a h}{\sqrt {1+{h^{\prime }}^{2}}}&=b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.494 |
|
| 16100 |
\begin{align*}
y {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.495 |
|