| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 7701 |
\begin{align*}
x^{\prime }&=-2 x+5 y \\
y^{\prime }&=-2 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.692 |
|
| 7702 |
\begin{align*}
4 y^{\prime \prime } x -y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.692 |
|
| 7703 |
\begin{align*}
x^{\prime }&=x-y-z \\
y^{\prime }&=x+3 y+z \\
z^{\prime }&=-3 x-6 y+6 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.692 |
|
| 7704 |
\begin{align*}
y^{\prime }&=x +2 z \\
z^{\prime }&=3 x +y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.692 |
|
| 7705 |
\begin{align*}
2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.693 |
|
| 7706 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.693 |
|
| 7707 |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}+x^{2} \left (x -y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.693 |
|
| 7708 |
\begin{align*}
y^{\prime } x +y x +y-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.693 |
|
| 7709 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.693 |
|
| 7710 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2}+3 \,{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}+2 t \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -{\frac {5}{18}} \\
x_{2} \left (0\right ) &= {\frac {47}{9}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.693 |
|
| 7711 |
\begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+11 y^{\prime \prime }-14 y^{\prime }+10 y&=-{\mathrm e}^{x} \left (\sin \left (x \right )+2 \cos \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| 7712 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-2 x_{2}+\delta \left (t -\pi \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| 7713 |
\begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=3 x_{2}+2 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-2 x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| 7714 |
\begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| 7715 |
\begin{align*}
2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| 7716 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (x^{2}-1\right ) y}{4}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| 7717 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y&=x \,{\mathrm e}^{x} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.694 |
|
| 7718 |
\begin{align*}
\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.694 |
|
| 7719 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| 7720 |
\begin{align*}
y^{\prime \prime } y^{\prime \prime \prime }&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.695 |
|
| 7721 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.695 |
|
| 7722 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\lambda y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| 7723 |
\begin{align*}
x^{\prime }&=2 y+z \\
y^{\prime }&=-x-3 y-z \\
z^{\prime }&=x+y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.696 |
|
| 7724 |
\begin{align*}
{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.696 |
|
| 7725 |
\begin{align*}
2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
0.696 |
|
| 7726 |
\begin{align*}
\left (x +1\right ) y^{\prime \prime }-3 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.696 |
|
| 7727 |
\begin{align*}
y^{\prime \prime }+2 y+t \sin \left (y\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.696 |
|
| 7728 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{2}^{\prime }&=-4 x_{1}-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=4 x_{1}+4 x_{2}+2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| 7729 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+2 x_{2}-x_{3} \\
x_{3}^{\prime }&=x_{1}-x_{2}+2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| 7730 |
\begin{align*}
2 {y^{\prime }}^{3}+y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.697 |
|
| 7731 |
\begin{align*}
x {y^{\prime }}^{2}+x y y^{\prime \prime }&=3 y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.697 |
|
| 7732 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.697 |
|
| 7733 |
\begin{align*}
\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.697 |
|
| 7734 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.697 |
|
| 7735 |
\begin{align*}
\left (2+x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.697 |
|
| 7736 |
\begin{align*}
\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (3 x +5\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| 7737 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\lambda \left (1+\lambda \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| 7738 |
\begin{align*}
y_{1}^{\prime }&=-y_{1}+y_{2}-y_{3} \\
y_{2}^{\prime }&=-2 y_{1}+2 y_{3} \\
y_{3}^{\prime }&=-y_{1}+3 y_{2}-y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| 7739 |
\begin{align*}
y_{1}^{\prime }&=-3 y_{1}-3 y_{2}+4 y_{3} \\
y_{2}^{\prime }&=4 y_{1}+5 y_{2}-8 y_{3} \\
y_{3}^{\prime }&=2 y_{1}+3 y_{2}-5 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| 7740 |
\begin{align*}
y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| 7741 |
\begin{align*}
\left (t^{2}-t -2\right ) x^{\prime \prime }+\left (1+t \right ) x^{\prime }-\left (-2+t \right ) x&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| 7742 |
\begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (16 x^{4}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| 7743 |
\begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| 7744 |
\begin{align*}
\cos \left (x \right ) y^{\prime }+\frac {y}{x}&=x \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✗ |
✗ |
0.698 |
|
| 7745 |
\begin{align*}
x^{\prime }&=-7 x+4 y+6 \,{\mathrm e}^{3 t} \\
y^{\prime }&=-5 x+2 y+6 \,{\mathrm e}^{2 t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| 7746 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+3 x_{3} \\
x_{2}^{\prime }&=6 x_{1}+4 x_{2}+6 x_{3} \\
x_{3}^{\prime }&=-5 x_{1}-2 x_{2}-4 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= -2 \\
x_{3} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| 7747 |
\begin{align*}
x^{\prime \prime }+9 x&=\delta \left (t -3 \pi \right )+\cos \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| 7748 |
\begin{align*}
x^{\prime }&=x+2 y+z \\
y^{\prime }&=6 x-y \\
z^{\prime }&=-x-2 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| 7749 |
\begin{align*}
{y^{\prime }}^{3}+{y^{\prime }}^{2}-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| 7750 |
\begin{align*}
16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| 7751 |
\begin{align*}
y^{\prime }+y-x^{\prime }+x&=t \\
x^{\prime }+y^{\prime }+x-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| 7752 |
\begin{align*}
4 y y^{\prime }-4 x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.700 |
|
| 7753 |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=10 x^{3}-2 x +5 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.700 |
|
| 7754 |
\begin{align*}
y^{\prime \prime }+y&=\frac {1}{\cos \left (x \right )^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 7755 |
\begin{align*}
x^{\prime }&=a x+10 y \\
y^{\prime }&=-x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| 7756 |
\begin{align*}
y_{1}^{\prime }&=-6 y_{1}-4 y_{2}-8 y_{3} \\
y_{2}^{\prime }&=-4 y_{1}-4 y_{3} \\
y_{3}^{\prime }&=-8 y_{1}-4 y_{2}-6 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 7757 |
\begin{align*}
f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.701 |
|
| 7758 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 7759 |
\begin{align*}
\sin \left (x \right ) y^{\prime }-y^{2} \sin \left (x \right )^{2}+\left (\cos \left (x \right )-3 \sin \left (x \right )\right ) y+4&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.701 |
|
| 7760 |
\begin{align*}
x^{2} y^{\prime \prime \prime }+5 y^{\prime \prime } x +4 y^{\prime }-\ln \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 7761 |
\begin{align*}
y&=\left (x +1\right ) {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 7762 |
\begin{align*}
x^{\prime }&=7 x+y-1-6 \,{\mathrm e}^{t} \\
y^{\prime }&=-4 x+3 y+4 \,{\mathrm e}^{t}-3 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 7763 |
\begin{align*}
y^{\prime \prime }+y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| 7764 |
\begin{align*}
2 y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 7765 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=-2 x_{2}+2 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= -2 \\
x_{3} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 7766 |
\begin{align*}
\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 7767 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 7768 |
\begin{align*}
y^{\prime }&=1-y \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 7769 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x +3 y&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 7770 |
\begin{align*}
x -\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 7771 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}-6 x_{3} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}-2 x_{3} \\
x_{3}^{\prime }&=4 x_{1}-2 x_{2}-4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| 7772 |
\begin{align*}
t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| 7773 |
\begin{align*}
x^{\prime }&=6 x-y \\
y^{\prime }&=5 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| 7774 |
\begin{align*}
-y^{\prime }+{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.703 |
|
| 7775 |
\begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 7776 |
\begin{align*}
y \left (1+{y^{\prime }}^{2}\right )&=2 y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 7777 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1} \\
x_{2}^{\prime }&=x_{2}-8 x_{3} \\
x_{3}^{\prime }&=2 x_{2}-7 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 7778 |
\begin{align*}
x^{\prime }&=5 x+9 y+2 \\
y^{\prime }&=-x+11 y+6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 7779 |
\begin{align*}
\left (4 x^{2}+1\right ) y^{\prime \prime }-8 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 7780 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.704 |
|
| 7781 |
\begin{align*}
2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.704 |
|
| 7782 |
\begin{align*}
\left (x +y^{2}\right ) y^{\prime \prime }-2 \left (x -y^{2}\right ) {y^{\prime }}^{3}+y^{\prime } \left (1+4 y y^{\prime }\right )&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.704 |
|
| 7783 |
\begin{align*}
x^{\prime }&=a x+b y \\
y^{\prime }&=c x+b y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 7784 |
\begin{align*}
2 y^{\prime \prime } x +y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 7785 |
\begin{align*}
x {y^{\prime }}^{3}&=1+y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 7786 |
\begin{align*}
s^{\prime }&=9 \sqrt {u} \\
s \left (4\right ) &= 16 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 7787 |
\begin{align*}
y^{\prime \prime }+\frac {\left (1-t \right ) y^{\prime }}{t}+\frac {\left (1-\cos \left (t \right )\right ) y}{t^{3}}&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.704 |
|
| 7788 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= \beta \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.705 |
|
| 7789 |
\begin{align*}
x^{\prime }-2 x+2 y^{\prime }&=-4 \,{\mathrm e}^{2 t} \\
2 x^{\prime }-3 x+3 y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 7790 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -\left (x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 7791 |
\begin{align*}
{y^{\prime }}^{2}+\left (a x +b y\right ) y^{\prime }+a b x y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 7792 |
\begin{align*}
2 y+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 7793 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1} \\
x_{2}^{\prime }&=x_{1}+3 x_{2} \\
x_{3}^{\prime }&=3 x_{3} \\
x_{4}^{\prime }&=2 x_{3}+3 x_{4} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
x_{4} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 7794 |
\begin{align*}
6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.706 |
|
| 7795 |
\begin{align*}
y^{\prime }&=-\frac {i \left (8 i x +16 y^{4}+8 y^{2} x^{2}+x^{4}\right )}{32 y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.706 |
|
| 7796 |
\begin{align*}
y^{\prime \prime \prime \prime }+16 y&=x^{2}-4 \cos \left (3 x \right ) \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 7797 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -3 y x&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 7798 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=5 \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{x}-4 \cos \left (x \right )+4 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 7799 |
\begin{align*}
y_{1}^{\prime }&=\frac {y_{1}}{3}+\frac {y_{2}}{3}-y_{3} \\
y_{2}^{\prime }&=-\frac {4 y_{1}}{3}-\frac {4 y_{2}}{3}+y_{3} \\
y_{3}^{\prime }&=-\frac {2 y_{1}}{3}+\frac {y_{2}}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 7800 |
\begin{align*}
t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.707 |
|