| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 13701 |
\begin{align*}
t^{2} x^{\prime \prime }-2 x&=t^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.334 |
|
| 13702 |
\begin{align*}
y^{\prime }+\left (\frac {1}{x}-1\right ) y&=-\frac {2}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.335 |
|
| 13703 |
\begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y&={\mathrm e}^{2 x} \sin \left (2 x \right )+2 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.335 |
|
| 13704 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.335 |
|
| 13705 |
\begin{align*}
7 x y^{\prime \prime }+10 y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.335 |
|
| 13706 |
\begin{align*}
4 y^{\prime \prime }+y&=2 \sec \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.335 |
|
| 13707 |
\begin{align*}
y^{\prime }&=t +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.335 |
|
| 13708 |
\begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| 13709 |
\begin{align*}
x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.336 |
|
| 13710 |
\begin{align*}
x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| 13711 |
\begin{align*}
{y^{\prime }}^{2}&=x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| 13712 |
\begin{align*}
x^{\prime }+3 x-y^{\prime }-y&=0 \\
2 x^{\prime }-9 x+y^{\prime }+4 y&=15 \,{\mathrm e}^{-3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| 13713 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| 13714 |
\begin{align*}
y^{\prime }&=2 y-y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.337 |
|
| 13715 |
\begin{align*}
x^{\prime \prime }+9 x&=t \sin \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.337 |
|
| 13716 |
\begin{align*}
{y^{\prime }}^{2} x -\left (x -a \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.337 |
|
| 13717 |
\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*} |
✓ |
✓ |
✓ |
✗ |
1.338 |
|
| 13718 |
\begin{align*}
y^{\prime }&=\frac {1}{2 y+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.338 |
|
| 13719 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime }&=3 \tan \left (x \right ) x^{2} \\
y \left (0\right ) &= \frac {\pi }{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| 13720 |
\begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y&=3 \sin \left (t \right )-5 \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| 13721 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| 13722 |
\begin{align*}
f \left ({y^{\prime }}^{2} x \right )+2 x y^{\prime }-y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.339 |
|
| 13723 |
\begin{align*}
x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.339 |
|
| 13724 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{2 x}+\frac {y}{4 x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| 13725 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| 13726 |
\begin{align*}
y^{\prime }+a y&=b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| 13727 |
\begin{align*}
x y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| 13728 |
\begin{align*}
x^{\prime \prime }&=\frac {1}{\left (t +1\right )^{3}} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.340 |
|
| 13729 |
\begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.340 |
|
| 13730 |
\begin{align*}
x^{\prime }&=x-12 y-14 z \\
y^{\prime }&=x+2 y-3 z \\
z^{\prime }&=x+y-2 z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 6 \\
z \left (0\right ) &= -7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.340 |
|
| 13731 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.340 |
|
| 13732 |
\begin{align*}
2 y y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.341 |
|
| 13733 |
\begin{align*}
y^{\prime }&=\left (x -2\right )^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| 13734 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| 13735 |
\begin{align*}
y-x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.342 |
|
| 13736 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c \left (a \,x^{2}+b -c \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.342 |
|
| 13737 |
\begin{align*}
y^{\prime \prime }+y&=\frac {1}{1+\sin \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| 13738 |
\begin{align*}
y^{\prime \prime }+25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| 13739 |
\begin{align*}
x^{\prime }&=\frac {x^{2}-x}{2 x-1} \\
x \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| 13740 |
\begin{align*}
y^{\prime \prime }&=9 x^{2}+2 x -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| 13741 |
\begin{align*}
y^{\prime \prime }&=9 x^{2}+2 x -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| 13742 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| 13743 |
\begin{align*}
y^{\left (6\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }+y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| 13744 |
\begin{align*}
x^{2}+y+y^{2}-x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| 13745 |
\begin{align*}
y^{\prime \prime }+9 y&=\sin \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.343 |
|
| 13746 |
\begin{align*}
y^{\prime \prime }+b y^{\prime }+c y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.343 |
|
| 13747 |
\begin{align*}
x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.344 |
|
| 13748 |
\begin{align*}
x^{\prime \prime }+10 x^{\prime }+25 x&=2^{t}+t \,{\mathrm e}^{-5 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.344 |
|
| 13749 |
\begin{align*}
y^{\prime \prime }+\frac {\left (1+{\mathrm e}^{x}\right ) y}{1-{\mathrm e}^{x}}&=0 \\
\end{align*}
Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
1.344 |
|
| 13750 |
\begin{align*}
y^{\prime \prime }+16 y&=\cot \left (4 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.344 |
|
| 13751 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-2 y-5 z+3 \\
z^{\prime }&=y+2 z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
1.344 |
|
| 13752 |
\begin{align*}
y^{\prime }&=y-y^{2}-\frac {1}{4} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.344 |
|
| 13753 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.344 |
|
| 13754 |
\begin{align*}
y^{\prime }&=x -y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.345 |
|
| 13755 |
\begin{align*}
y^{\prime }&=-{\mathrm e}^{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.345 |
|
| 13756 |
\begin{align*}
\left (x^{2}+1\right ) {y^{\prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.346 |
|
| 13757 |
\begin{align*}
2 y^{\prime \prime }-7 y^{\prime }+3&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.346 |
|
| 13758 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+2 x_{2}-x_{4} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+2 x_{4} \\
x_{3}^{\prime }&=3 x_{3} \\
x_{4}^{\prime }&=-x_{1}+2 x_{2}+2 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.346 |
|
| 13759 |
\begin{align*}
\left (b +a y\right ) \left (1+{y^{\prime }}^{2}\right )-c&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.347 |
|
| 13760 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.347 |
|
| 13761 |
\begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+26 y^{\prime \prime }-40 y^{\prime }+25 y&={\mathrm e}^{2 x} \left (3 \cos \left (x \right )-\left (1+3 x \right ) \sin \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.348 |
|
| 13762 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=3 y-3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.348 |
|
| 13763 |
\begin{align*}
-a^{2} y+y^{\prime \prime }&={\mathrm e}^{a x}+{\mathrm e}^{n x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.348 |
|
| 13764 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.348 |
|
| 13765 |
\begin{align*}
y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.348 |
|
| 13766 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+9 x_{4} \\
x_{2}^{\prime }&=4 x_{1}+2 x_{2}-10 x_{4} \\
x_{3}^{\prime }&=-x_{3}+8 x_{4} \\
x_{4}^{\prime }&=x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.349 |
|
| 13767 |
\begin{align*}
-y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.349 |
|
| 13768 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=\cos \left (x \right ) {\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.349 |
|
| 13769 |
\begin{align*}
x^{\prime }&=x+y-z \\
y^{\prime }&=2 x+3 y-4 z \\
z^{\prime }&=4 x+y-4 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.350 |
|
| 13770 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.350 |
|
| 13771 |
\begin{align*}
y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+3\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.350 |
|
| 13772 |
\begin{align*}
x y^{\prime }+1&={\mathrm e}^{x -y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.350 |
|
| 13773 |
\begin{align*}
y^{\prime }+y^{2}+5 y-6&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.351 |
|
| 13774 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.351 |
|
| 13775 |
\begin{align*}
y^{\prime }&=-\frac {4}{x^{2}} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.351 |
|
| 13776 |
\begin{align*}
x_{1}^{\prime }&=7 x_{1}-x_{4} \\
x_{2}^{\prime }&=6 x_{2} \\
x_{3}^{\prime }&=-x_{3} \\
x_{4}^{\prime }&=2 x_{1}+5 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.352 |
|
| 13777 |
\begin{align*}
y^{\prime \prime }-y&=\operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.352 |
|
| 13778 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-7 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.352 |
|
| 13779 |
\begin{align*}
b y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.352 |
|
| 13780 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.352 |
|
| 13781 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=3-4 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.352 |
|
| 13782 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.352 |
|
| 13783 |
\begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{2} \\
x_{3}^{\prime }&=3 x_{2}+3 x_{3} \\
x_{4}^{\prime }&=4 x_{3}+4 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.353 |
|
| 13784 |
\begin{align*}
m y^{\prime \prime }+c y^{\prime }+k y&=F_{0} \cos \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.353 |
|
| 13785 |
\begin{align*}
y^{\prime }&=-x +y \\
y \left (4\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.354 |
|
| 13786 |
\begin{align*}
y^{\prime \prime }&=A \,x^{a} y^{b} {y^{\prime }}^{c} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.354 |
|
| 13787 |
\begin{align*}
y^{\prime }-x y^{\prime \prime }+{y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.354 |
|
| 13788 |
\begin{align*}
x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.354 |
|
| 13789 |
\begin{align*}
\left (\beta \,x^{2}+\alpha x +1\right ) y^{\prime \prime }+\left (\delta x +\gamma \right ) y^{\prime }+\epsilon y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.355 |
|
| 13790 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=x^{2} {\mathrm e}^{-x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.355 |
|
| 13791 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.355 |
|
| 13792 |
\begin{align*}
x y^{\prime \prime }-{y^{\prime }}^{3}-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.355 |
|
| 13793 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.355 |
|
| 13794 |
\begin{align*}
x^{2} y^{\prime \prime }-2 a x y^{\prime }+\left (-b^{2} x^{2}+a \left (a +1\right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.356 |
|
| 13795 |
\begin{align*}
y^{\prime }&=\frac {1+y^{2}}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.356 |
|
| 13796 |
\begin{align*}
y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y&=-3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.356 |
|
| 13797 |
\begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y \left (\frac {\pi }{2}\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.356 |
|
| 13798 |
\begin{align*}
y^{\prime \prime }+b y^{\prime }+y&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.356 |
|
| 13799 |
\begin{align*}
x y^{\prime } \left (y y^{\prime \prime }-{y^{\prime }}^{2}\right )-y {y^{\prime }}^{2}&=x^{4} y^{3} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.356 |
|
| 13800 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=10 x^{4}+2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.357 |
|