| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10701 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.443 |
|
| 10702 |
\begin{align*}
x^{\prime \prime }+4 x&=\delta \left (t \right )+\delta \left (t -\pi \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.444 |
|
| 10703 |
\begin{align*}
\left (1+x^{2}+y^{2}\right ) y^{\prime }+2 y x +x^{2}+3&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.444 |
|
| 10704 |
\begin{align*}
y^{\prime \prime } x -2 \left (2+x \right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.444 |
|
| 10705 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.444 |
|
| 10706 |
\begin{align*}
9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.444 |
|
| 10707 |
\begin{align*}
y^{3} y^{\prime \prime }&=k \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.445 |
|
| 10708 |
\begin{align*}
y^{\prime \prime }+y&=\delta \left (t -2 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.446 |
|
| 10709 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{2 x}+b \,{\mathrm e}^{x}+c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.446 |
|
| 10710 |
\begin{align*}
y^{\prime }&=\frac {x \,{\mathrm e}^{x}}{2 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.446 |
|
| 10711 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.447 |
|
| 10712 |
\begin{align*}
y^{\prime }+y&={\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.448 |
|
| 10713 |
\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*} |
✓ |
✓ |
✓ |
✗ |
1.448 |
|
| 10714 |
\begin{align*}
y^{\prime \prime }-4 y&=31 \\
y \left (0\right ) &= -9 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.448 |
|
| 10715 |
\begin{align*}
-y+y^{\prime } x&=x^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.449 |
|
| 10716 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=\left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.449 |
|
| 10717 |
\begin{align*}
y^{\prime \prime }-3&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.449 |
|
| 10718 |
\begin{align*}
y^{\prime \prime }-m^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.450 |
|
| 10719 |
\begin{align*}
y&=a y^{\prime }+b {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.450 |
|
| 10720 |
\begin{align*}
-2 y^{\prime }+\left (a -x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.451 |
|
| 10721 |
\begin{align*}
2 y y^{\prime \prime }-3 {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.451 |
|
| 10722 |
\begin{align*}
y^{\prime }&=a y^{2}+b \,x^{2 n}+c \,x^{n -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.451 |
|
| 10723 |
\begin{align*}
y^{\prime }-\frac {2 y}{t}&=2 t^{2} \\
y \left (-2\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.451 |
|
| 10724 |
\begin{align*}
\left (-y^{\prime } x +y\right )^{2}&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.451 |
|
| 10725 |
\begin{align*}
y^{\prime } t +y&={\mathrm e}^{t} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.451 |
|
| 10726 |
\begin{align*}
3 y^{2} y^{\prime }+y^{3}&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.452 |
|
| 10727 |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.452 |
|
| 10728 |
\begin{align*}
b \,{\mathrm e}^{2 a x} y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.452 |
|
| 10729 |
\begin{align*}
x^{\prime }&=3 y-3 x \\
y^{\prime }&=x+2 y-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.452 |
|
| 10730 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=2 \delta \left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.453 |
|
| 10731 |
\begin{align*}
2 y y^{\prime } x +a +y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.454 |
|
| 10732 |
\begin{align*}
y_{1}^{\prime }&=y_{1}+2 y_{2}-3 y_{3} \\
y_{2}^{\prime }&=-3 y_{1}+4 y_{2}-2 y_{3} \\
y_{3}^{\prime }&=2 y_{1}+y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.454 |
|
| 10733 |
\begin{align*}
x^{\prime \prime }+4 x^{3}&=0 \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.454 |
|
| 10734 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (2+x \right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.455 |
|
| 10735 |
\begin{align*}
4 x {y^{\prime }}^{2}+4 y y^{\prime }-y^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.455 |
|
| 10736 |
\begin{align*}
{y^{\prime }}^{2}-y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.455 |
|
| 10737 |
\begin{align*}
y-2 y^{\prime } x -y {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.455 |
|
| 10738 |
\begin{align*}
y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.455 |
|
| 10739 |
\begin{align*}
y^{\prime }-y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.455 |
|
| 10740 |
\begin{align*}
y+y^{\prime }&=5 \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.456 |
|
| 10741 |
\begin{align*}
2 y+y^{\prime }&={\mathrm e}^{-x^{2}-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.456 |
|
| 10742 |
\begin{align*}
-5 y-3 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.456 |
|
| 10743 |
\begin{align*}
4 y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= \beta \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.457 |
|
| 10744 |
\begin{align*}
x_{1}^{\prime }&=-x_{2} \\
x_{2}^{\prime }&=x_{1} \\
x_{3}^{\prime }&=x_{1}+2 x_{3}+x_{4} \\
x_{4}^{\prime }&=x_{2}+2 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.457 |
|
| 10745 |
\begin{align*}
y^{\prime \prime }&=-\frac {f^{\prime }\left (x \right ) y^{\prime }}{2 f \left (x \right )}-\frac {g \left (x \right ) y}{f \left (x \right )} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.457 |
|
| 10746 |
\begin{align*}
a y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.457 |
|
| 10747 |
\begin{align*}
-\left (a^{2}+1\right ) y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.457 |
|
| 10748 |
\begin{align*}
y^{\prime \prime }&=1-\cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.457 |
|
| 10749 |
\begin{align*}
y^{\prime }&=y^{2}-y^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.457 |
|
| 10750 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.458 |
|
| 10751 |
\begin{align*}
y^{\left (5\right )}+2 y^{\prime \prime \prime }+y^{\prime }-a x -b \sin \left (x \right )-c \cos \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.458 |
|
| 10752 |
\begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{-x} \\
y \left (2\right ) &= 0 \\
y^{\prime }\left (2\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.459 |
|
| 10753 |
\begin{align*}
y&=y^{\prime } x +x^{2} {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.460 |
|
| 10754 |
\begin{align*}
7 t^{2} x^{\prime }&=3 x-2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.460 |
|
| 10755 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.461 |
|
| 10756 |
\begin{align*}
y^{\prime \prime }&=2+x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.461 |
|
| 10757 |
\begin{align*}
x^{2} \left (1+{y^{\prime }}^{2}\right )^{3}-a^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.461 |
|
| 10758 |
\begin{align*}
y^{\prime }-y-{\mathrm e}^{3 x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.462 |
|
| 10759 |
\begin{align*}
x^{\prime \prime }+\pi ^{2} x&=\pi ^{2} \operatorname {Heaviside}\left (1-t \right ) \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.462 |
|
| 10760 |
\begin{align*}
i^{\prime }+2 i&=10 \,{\mathrm e}^{-2 t} \\
i \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.462 |
|
| 10761 |
\begin{align*}
y^{\prime \prime } x +y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.462 |
|
| 10762 |
\begin{align*}
y^{\prime \prime }&=\sec \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.463 |
|
| 10763 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=6 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 11 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.464 |
|
| 10764 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.464 |
|
| 10765 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.464 |
|
| 10766 |
\begin{align*}
x_{1}^{\prime }&=11 x_{1}-x_{2}+26 x_{3}+6 x_{4}-3 x_{5} \\
x_{2}^{\prime }&=3 x_{2} \\
x_{3}^{\prime }&=-9 x_{1}-24 x_{3}-6 x_{4}+3 x_{5} \\
x_{4}^{\prime }&=3 x_{1}+9 x_{3}+5 x_{4}-x_{5} \\
x_{5}^{\prime }&=-48 x_{1}-3 x_{2}-138 x_{3}-30 x_{4}+18 x_{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.465 |
|
| 10767 |
\begin{align*}
y^{\prime }-3 y&=12 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.465 |
|
| 10768 |
\begin{align*}
y^{\prime }&=f \left (x \right ) g \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.465 |
|
| 10769 |
\begin{align*}
2 y^{\prime \prime } x +\left (1-x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.466 |
|
| 10770 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.466 |
|
| 10771 |
\begin{align*}
x^{\prime \prime }&=50 \sin \left (5 t \right ) \\
x \left (0\right ) &= 8 \\
x^{\prime }\left (0\right ) &= -10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.467 |
|
| 10772 |
\begin{align*}
y^{\prime }+\tan \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.467 |
|
| 10773 |
\begin{align*}
2 y+y^{\prime }&=b \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.467 |
|
| 10774 |
\begin{align*}
y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.467 |
|
| 10775 |
\begin{align*}
x \left (x +1\right )^{2} y y^{\prime \prime }-x \left (x +1\right )^{2} {y^{\prime }}^{2}+2 \left (x +1\right )^{2} y y^{\prime }-a \left (2+x \right ) y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.467 |
|
| 10776 |
\begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.467 |
|
| 10777 |
\begin{align*}
y^{\prime }+y \ln \left (y\right )&=t y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.467 |
|
| 10778 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.468 |
|
| 10779 |
\begin{align*}
y^{2} y^{\prime }+x \left (2-y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.469 |
|
| 10780 |
\begin{align*}
2 x^{2} y \left (-1+y\right ) y^{\prime \prime }-x^{2} \left (3 y-1\right ) {y^{\prime }}^{2}+2 x y \left (-1+y\right ) y^{\prime }+\left (a y^{2}+b \right ) \left (-1+y\right )^{3}+c x y^{2} \left (-1+y\right )+d \,x^{2} y^{2} \left (1+y\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.469 |
|
| 10781 |
\begin{align*}
y^{\prime \prime }+y&=\frac {1}{\sin \left (x \right )^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.470 |
|
| 10782 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+3 x_{2}+2 x_{3}+\sin \left (t \right ) \\
x_{2}^{\prime }&=-x_{1}+2 x_{2}+x_{3} \\
x_{3}^{\prime }&=4 x_{1}-x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.471 |
|
| 10783 |
\begin{align*}
y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.471 |
|
| 10784 |
\begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.472 |
|
| 10785 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+k y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.472 |
|
| 10786 |
\begin{align*}
y^{\prime }+y x&=x^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.472 |
|
| 10787 |
\begin{align*}
y^{\prime }-\sqrt {\frac {a y^{2}+b y+c}{a \,x^{2}+b x +c}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.473 |
|
| 10788 |
\begin{align*}
x^{4} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.473 |
|
| 10789 |
\begin{align*}
y^{\prime }&=4 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.473 |
|
| 10790 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.473 |
|
| 10791 |
\begin{align*}
x^{2} {y^{\prime }}^{2}+x \left (x^{3}-2 y\right ) y^{\prime }-\left (2 x^{3}-y\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.474 |
|
| 10792 |
\begin{align*}
x \left (1-2 x \right ) y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+18 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| 10793 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| 10794 |
\begin{align*}
\left (1+t \right ) y^{\prime }+y&=0 \\
y \left (1\right ) &= -9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| 10795 |
\begin{align*}
y^{\prime }&=x^{2}-y-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.475 |
|
| 10796 |
\begin{align*}
\left (x^{2}+y^{2}+x \right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.475 |
|
| 10797 |
\begin{align*}
y^{\prime }&=3 y \left (y-2\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.475 |
|
| 10798 |
\begin{align*}
y^{\prime }&={\mathrm e}^{4 x +3 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.475 |
|
| 10799 |
\begin{align*}
2 y^{3} y^{\prime }+x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.476 |
|
| 10800 |
\begin{align*}
y^{\prime \prime }&=2 y^{3} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.476 |
|