| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 17101 |
\begin{align*}
y^{\prime }+4 y&=8 \cos \left (4 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.650 |
|
| 17102 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.650 |
|
| 17103 |
\begin{align*}
y^{\prime }-y \tan \left (x \right )&=x \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.651 |
|
| 17104 |
\begin{align*}
y-x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.651 |
|
| 17105 |
\begin{align*}
y^{\prime }&=x +y \\
y \left (-2\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.651 |
|
| 17106 |
\begin{align*}
2 y y^{\prime }&={\mathrm e}^{x -y^{2}} \\
y \left (4\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.651 |
|
| 17107 |
\begin{align*}
y^{\prime }&=y \ln \left (y+2\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.653 |
|
| 17108 |
\begin{align*}
{y^{\prime }}^{2} x -2 y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.654 |
|
| 17109 |
\begin{align*}
y^{\prime \prime }+36 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.654 |
|
| 17110 |
\begin{align*}
y^{\prime \prime }-2 x^{2} y-x^{4}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.655 |
|
| 17111 |
\begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.655 |
|
| 17112 |
\begin{align*}
y^{\prime \prime }-y&=12 \,{\mathrm e}^{x} x^{2}+3 \,{\mathrm e}^{2 x}+10 \cos \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.656 |
|
| 17113 |
\begin{align*}
a^{2}-2 y x -y^{2}-\left (x +y\right )^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.656 |
|
| 17114 |
\begin{align*}
y y^{\prime }&=1+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.656 |
|
| 17115 |
\begin{align*}
{y^{\prime }}^{2}&=\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.657 |
|
| 17116 |
\begin{align*}
x y^{2}+x \sin \left (x \right )^{2}-\sin \left (2 x \right )-2 y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.657 |
|
| 17117 |
\begin{align*}
\left (x +2\right ) y^{\prime }+4 y&=\frac {2 x^{2}+1}{x \left (x +2\right )^{3}} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.658 |
|
| 17118 |
\begin{align*}
2 \left (b x +3 a \right ) y-2 x \left (b x +2 a \right ) y^{\prime }+x^{2} \left (b x +a \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.658 |
|
| 17119 |
\begin{align*}
y y^{\prime }+x y^{2}-8 x&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.658 |
|
| 17120 |
\begin{align*}
\frac {3 x^{2}+y^{2}}{y^{2}}-\frac {\left (2 x^{3}+5 y\right ) y^{\prime }}{y^{3}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.658 |
|
| 17121 |
\begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=x -\left (5 x^{2}+3\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.659 |
|
| 17122 |
\begin{align*}
2 y+t y^{\prime }&=\frac {\sin \left (t \right )}{t} \\
y \left (-\frac {\pi }{2}\right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.660 |
|
| 17123 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=3 \sqrt {x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.660 |
|
| 17124 |
\begin{align*}
-b \left (b \,x^{2}+a \right ) y+a y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.661 |
|
| 17125 |
\begin{align*}
y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+y \sin \left (x \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.661 |
|
| 17126 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0<t <1 \\ 0 & 1<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.662 |
|
| 17127 |
\begin{align*}
3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.662 |
|
| 17128 |
\begin{align*}
y^{\prime \prime }&=f \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.663 |
|
| 17129 |
\begin{align*}
y^{3} y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.663 |
|
| 17130 |
\begin{align*}
x y^{2} \left (x y^{\prime }+y\right )&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.663 |
|
| 17131 |
\begin{align*}
y^{\prime }&=-\tan \left (t \right ) y+\sec \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.664 |
|
| 17132 |
\begin{align*}
-\left (4 x^{2}+1\right ) y+4 x y^{\prime }+4 x^{2} y^{\prime \prime }&=4 x^{{3}/{2}} {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.664 |
|
| 17133 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x^{2}}}{y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.664 |
|
| 17134 |
\begin{align*}
y^{\prime }&=\frac {y}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.665 |
|
| 17135 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=a x \\
y \left (0\right ) &= 2 a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.665 |
|
| 17136 |
\begin{align*}
y^{\prime }+y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.665 |
|
| 17137 |
\begin{align*}
\cos \left (y\right ) y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.665 |
|
| 17138 |
\begin{align*}
y^{\prime }+x y^{2}-x^{3} y-2 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.666 |
|
| 17139 |
\begin{align*}
y^{\prime }&=3-6 x +y-2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.667 |
|
| 17140 |
\begin{align*}
y^{\prime }&=\sec \left (x \right )-y \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.667 |
|
| 17141 |
\begin{align*}
{y^{\prime }}^{4}&=\left (y-a \right )^{3} \left (y-b \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.667 |
|
| 17142 |
\begin{align*}
y^{\prime \prime }&=\operatorname {c1} \cos \left (a x \right )+\operatorname {c2} \sin \left (b x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.667 |
|
| 17143 |
\begin{align*}
x y^{\prime \prime }+n y^{\prime }+b \,x^{1-2 n} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.667 |
|
| 17144 |
\begin{align*}
\left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.668 |
|
| 17145 |
\begin{align*}
y^{\prime \prime }-\left (n \left (n +1\right ) k^{2} \operatorname {JacobiSN}\left (x , k\right )^{2}+b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.668 |
|
| 17146 |
\begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.669 |
|
| 17147 |
\begin{align*}
y^{\prime }+\cos \left (x \right ) y-\frac {\sin \left (2 x \right )}{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.669 |
|
| 17148 |
\begin{align*}
\left (x y^{\prime }-y\right )^{2}+x^{2} y y^{\prime \prime }&=3 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.671 |
|
| 17149 |
\begin{align*}
x y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.671 |
|
| 17150 |
\begin{align*}
x y^{\prime }-\frac {y}{\ln \left (x \right )}&=x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.671 |
|
| 17151 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.673 |
|
| 17152 |
\begin{align*}
{y^{\prime }}^{3}-\left (y-a \right )^{2} \left (y-b \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.674 |
|
| 17153 |
\begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.674 |
|
| 17154 |
\begin{align*}
x^{\prime }+x \cot \left (y \right )&=\sec \left (y \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.674 |
|
| 17155 |
\begin{align*}
x y^{\prime }+\frac {y}{2 x +3}&=\ln \left (x -2\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.674 |
|
| 17156 |
\begin{align*}
2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.674 |
|
| 17157 |
\begin{align*}
x y^{\prime \prime }-y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.675 |
|
| 17158 |
\begin{align*}
y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.675 |
|
| 17159 |
\begin{align*}
y^{\prime }&=t^{2}+t^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.676 |
|
| 17160 |
\begin{align*}
x^{\prime \prime }+4 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.676 |
|
| 17161 |
\begin{align*}
y^{\prime }&=y \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.677 |
|
| 17162 |
\begin{align*}
y^{\prime }&=\frac {t y}{t^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.677 |
|
| 17163 |
\begin{align*}
y^{2} x^{\prime }+\left (y^{2}+2 y \right ) x&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.678 |
|
| 17164 |
\begin{align*}
f \left (y\right ) y^{\prime }+g \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.678 |
|
| 17165 |
\begin{align*}
-4 y x +x^{2} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.679 |
|
| 17166 |
\begin{align*}
y^{\prime \prime }+25 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.679 |
|
| 17167 |
\begin{align*}
y^{\prime }&=-2 y t +4 \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.681 |
|
| 17168 |
\begin{align*}
y^{\prime }&=x^{2}+2 x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.681 |
|
| 17169 |
\begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.681 |
|
| 17170 |
\begin{align*}
y^{\prime \prime }&=A y^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.682 |
|
| 17171 |
\begin{align*}
y^{\prime }&=y \left (-3+y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.683 |
|
| 17172 |
\begin{align*}
6 y-4 \left (x +a \right ) y^{\prime }+\left (x +a \right )^{2} y^{\prime \prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.684 |
|
| 17173 |
\begin{align*}
y^{3} y^{\prime \prime }&=4 y^{4}-4 \\
y \left (0\right ) &= \sqrt {2} \\
y^{\prime }\left (0\right ) &= \sqrt {2} \\
\end{align*} |
✓ |
✗ |
✓ |
✓ |
2.684 |
|
| 17174 |
\begin{align*}
x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.685 |
|
| 17175 |
\begin{align*}
-x y^{\prime }+y&=b \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.685 |
|
| 17176 |
\begin{align*}
y x +x^{2}-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.685 |
|
| 17177 |
\begin{align*}
2 x \left (1-x \right ) y^{\prime }+x +\left (1-2 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.687 |
|
| 17178 |
\begin{align*}
y^{\prime }&=x -y \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.687 |
|
| 17179 |
\begin{align*}
y^{\prime \prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.687 |
|
| 17180 |
\begin{align*}
y^{\prime }-y&=x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.688 |
|
| 17181 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+2 x_{3} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
x_{3}^{\prime }&=-2 x_{1}-x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= -1 \\
x_{3} \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.688 |
|
| 17182 |
\begin{align*}
x^{\prime }&=2 x-3 y \\
y^{\prime }&=5 x+6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.689 |
|
| 17183 |
\begin{align*}
x y^{\prime }+y&={\mathrm e}^{x} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.690 |
|
| 17184 |
\begin{align*}
y^{\prime \prime }-36 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.691 |
|
| 17185 |
\begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.691 |
|
| 17186 |
\begin{align*}
x y^{\prime }&=x \sin \left (x \right )-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.692 |
|
| 17187 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.693 |
|
| 17188 |
\begin{align*}
y^{\prime }-\frac {2 x y}{x^{2}+1}&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.694 |
|
| 17189 |
\begin{align*}
\left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.694 |
|
| 17190 |
\begin{align*}
y^{\prime \prime }-4 y&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.694 |
|
| 17191 |
\begin{align*}
\left (x \cos \left (\frac {y}{x}\right )+\sin \left (\frac {y}{x}\right ) y\right ) y+\left (x \cos \left (\frac {y}{x}\right )-\sin \left (\frac {y}{x}\right ) y\right ) x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.694 |
|
| 17192 |
\begin{align*}
y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.694 |
|
| 17193 |
\begin{align*}
3 y+y^{\prime }&={\mathrm e}^{t} \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.694 |
|
| 17194 |
\begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.694 |
|
| 17195 |
\begin{align*}
y+\left (3 x +2\right ) y^{\prime }+x \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.695 |
|
| 17196 |
\begin{align*}
y^{\prime }-\left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.695 |
|
| 17197 |
\begin{align*}
y^{\prime } y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.695 |
|
| 17198 |
\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*} |
✓ |
✓ |
✓ |
✗ |
2.696 |
|
| 17199 |
\begin{align*}
x^{2} y^{\prime \prime }-7 x y^{\prime }+25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.696 |
|
| 17200 |
\begin{align*}
y^{\prime }&=a \sin \left (b x +c \right )+k y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.697 |
|