| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 8001 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{3} \\
x_{2}^{\prime }&=2 x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{3} \\
x_{4}^{\prime }&=-x_{3}+2 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| 8002 |
\begin{align*}
x_{1}^{\prime }&=-x_{1} \\
x_{2}^{\prime }&=x_{1}+5 x_{2}-x_{3} \\
x_{3}^{\prime }&=x_{1}+6 x_{2}-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| 8003 |
\begin{align*}
{y^{\prime }}^{2}&=a^{2} y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| 8004 |
\begin{align*}
y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| 8005 |
\begin{align*}
y^{\prime \prime }+\left ({\mathrm e}^{-2 x}-\frac {1}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| 8006 |
\begin{align*}
y \ln \left (y\right )-2 y x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.736 |
|
| 8007 |
\begin{align*}
y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| 8008 |
\begin{align*}
x^{\prime }&=3 x+2 y+2 z \\
y^{\prime }&=x+4 y+z \\
z^{\prime }&=-2 x-4 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| 8009 |
\begin{align*}
x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (x^{2}+3\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| 8010 |
\begin{align*}
{y^{\prime }}^{3}-a x y y^{\prime }+2 a y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.737 |
|
| 8011 |
\begin{align*}
4 {y^{\prime }}^{3}+4 y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| 8012 |
\begin{align*}
x^{\prime }&=-\lambda x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| 8013 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| 8014 |
\begin{align*}
x^{\prime }&=-2 x+y+t \\
y^{\prime }&=-4 x+3 y-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.738 |
|
| 8015 |
\begin{align*}
x +y+1-\left (3-x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.738 |
|
| 8016 |
\begin{align*}
\left (2+x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.738 |
|
| 8017 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime } x +3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.739 |
|
| 8018 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| 8019 |
\begin{align*}
x_{1}^{\prime }&=35 x_{1}-12 x_{2}+4 x_{3}+30 x_{4} \\
x_{2}^{\prime }&=22 x_{1}-8 x_{2}+3 x_{3}+19 x_{4} \\
x_{3}^{\prime }&=-10 x_{1}+3 x_{2}-9 x_{4} \\
x_{4}^{\prime }&=-27 x_{1}+9 x_{2}-3 x_{3}-23 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| 8020 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y \ln \left (x \right )&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| 8021 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+4 x_{3} \\
x_{2}^{\prime }&=2 x_{2} \\
x_{3}^{\prime }&=-4 x_{1}-5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| 8022 |
\begin{align*}
y^{\prime \prime }&=\operatorname {g3} \left (x \right )+\operatorname {g2} \left (x \right ) y+\operatorname {g1} \left (x \right ) y^{2}+\operatorname {g0} \left (x \right ) y^{3}+\left (\operatorname {f1} \left (x \right )+\operatorname {f0} \left (x \right ) y\right ) y^{\prime } \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.740 |
|
| 8023 |
\begin{align*}
\left (\phi ^{\prime }-\frac {\phi ^{2}}{2}\right ) \sin \left (\theta \right )^{2}-\phi \sin \left (\theta \right ) \cos \left (\theta \right )&=\frac {\cos \left (2 \theta \right )}{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.740 |
|
| 8024 |
\begin{align*}
x^{\prime }&=x+y-z \\
y^{\prime }&=y+z-x \\
z^{\prime }&=x-y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| 8025 |
\begin{align*}
-{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.740 |
|
| 8026 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| 8027 |
\begin{align*}
z y^{\prime \prime }-2 y^{\prime }+9 z^{5} y&=0 \\
\end{align*} Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
0.741 |
|
| 8028 |
\begin{align*}
y^{\prime \prime }+\frac {y}{4 x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.741 |
|
| 8029 |
\begin{align*}
y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.741 |
|
| 8030 |
\begin{align*}
\left (2 x^{2}+2\right ) y^{\prime \prime }+2 y^{\prime } x -3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.741 |
|
| 8031 |
\begin{align*}
x^{4} y^{\prime \prime }&=-4 y^{2}+x^{2} y^{\prime } \left (x +y^{\prime }\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.742 |
|
| 8032 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.742 |
|
| 8033 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x +1 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.742 |
|
| 8034 |
\begin{align*}
\left (3 x y^{3}-4 y x +y\right ) y^{\prime }+y^{2} \left (y^{2}-2\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.742 |
|
| 8035 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.742 |
|
| 8036 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-4 x_{2}-2 x_{4} \\
x_{2}^{\prime }&=x_{2} \\
x_{3}^{\prime }&=6 x_{1}-12 x_{2}-x_{3}-6 x_{4} \\
x_{4}^{\prime }&=-4 x_{2}-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*} |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| 8037 |
\begin{align*}
x_{1}^{\prime }&=x_{3} \\
x_{2}^{\prime }&=x_{4} \\
x_{3}^{\prime }&=-2 x_{1}+2 x_{2}-3 x_{3}+x_{4} \\
x_{4}^{\prime }&=2 x_{1}-2 x_{2}+x_{3}-3 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| 8038 |
\begin{align*}
4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| 8039 |
\begin{align*}
{y^{\prime }}^{3}-\left (b x +a \right ) y^{\prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.743 |
|
| 8040 |
\begin{align*}
9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| 8041 |
\begin{align*}
y^{\prime }&=y^{2}-4 y-12 \\
y \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.743 |
|
| 8042 |
\begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (0\right ) &= \pi \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.743 |
|
| 8043 |
\begin{align*}
y^{\prime \prime }+y&=1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| 8044 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\left (-n^{2}+x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| 8045 |
\begin{align*}
y^{\prime \prime } x +\left (3 x +5\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| 8046 |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }+2 x&=2 \delta \left (t -\pi \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| 8047 |
\begin{align*}
2 y^{2} {\mathrm e}^{2 x}+3 x^{2}+2 y \,{\mathrm e}^{2 x} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| 8048 |
\begin{align*}
y^{\prime \prime }-y&=\sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| 8049 |
\begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (-x^{3}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| 8050 |
\begin{align*}
12 y^{\prime \prime }+8 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| 8051 |
\begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }+\left (2 x +\frac {2}{x}\right ) y^{\prime }+2 x^{2} y&=\frac {4 x^{2}+2 x +10}{x^{4}} \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.744 |
|
| 8052 |
\begin{align*}
y^{\prime \prime }&=2 y y^{\prime } \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.745 |
|
| 8053 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime } x -4 y&={\mathrm e}^{x} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.745 |
|
| 8054 |
\begin{align*}
\left (2+4 x \right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.745 |
|
| 8055 |
\begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} -4 t +8 \pi & 0<t <2 \pi \\ 0 & 2<t \end {array}\right . \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.745 |
|
| 8056 |
\begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=z-x \\
z^{\prime }&=x+3 y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.745 |
|
| 8057 |
\begin{align*}
t^{3} y^{\prime \prime }+\sin \left (t^{3}\right ) y^{\prime }+t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.746 |
|
| 8058 |
\begin{align*}
4 y^{\prime \prime } x +\frac {y^{\prime }}{2}+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| 8059 |
\begin{align*}
\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.746 |
|
| 8060 |
\begin{align*}
\left (2 x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| 8061 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| 8062 |
\begin{align*}
y^{\prime }&=y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| 8063 |
\begin{align*}
x^{\prime \prime }+6 x^{\prime }+9 x&=f \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| 8064 |
\begin{align*}
x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.747 |
|
| 8065 |
\begin{align*}
y^{\prime }&=y^{2}-y^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| 8066 |
\begin{align*}
{y^{\prime }}^{3}+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.747 |
|
| 8067 |
\begin{align*}
y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=\left (1+\ln \left (x \right )\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| 8068 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}+x_{2}-2 x_{3} \\
x_{2}^{\prime }&=4 x_{1}+x_{2} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.748 |
|
| 8069 |
\begin{align*}
y^{\prime \prime } x +\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.748 |
|
| 8070 |
\begin{align*}
y^{\prime \prime }+y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.748 |
|
| 8071 |
\begin{align*}
4 t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.749 |
|
| 8072 |
\begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=-y_{1}+y_{3} \\
y_{3}^{\prime }&=-y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.749 |
|
| 8073 |
\begin{align*}
y^{\prime \prime }&=2 y y^{\prime } \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.749 |
|
| 8074 |
\begin{align*}
3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| 8075 |
\begin{align*}
-y+y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| 8076 |
\begin{align*}
\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.750 |
|
| 8077 |
\begin{align*}
{y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.750 |
|
| 8078 |
\begin{align*}
y^{\prime }&=-\frac {i \left (16 i x^{2}+16 y^{4}+8 y^{2} x^{4}+x^{8}\right ) x}{32 y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.750 |
|
| 8079 |
\begin{align*}
y^{\prime \prime }+4 y&=2 \delta \left (t -\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| 8080 |
\begin{align*}
y_{1}^{\prime }&=4 y_{2} \\
y_{2}^{\prime }&=-y_{1} \\
y_{3}^{\prime }&=y_{1}+4 y_{2}-y_{3} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= 1 \\
y_{3} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| 8081 |
\begin{align*}
2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| 8082 |
\begin{align*}
x^{2} {y^{\prime }}^{2}-3 y y^{\prime } x +x^{3}+2 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.751 |
|
| 8083 |
\begin{align*}
x^{\prime }&=4 x+5 y \\
y^{\prime }&=-2 x+6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| 8084 |
\begin{align*}
y+y^{\prime }&=\operatorname {Heaviside}\left (-2+t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| 8085 |
\begin{align*}
2 y^{\prime \prime } x -y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.752 |
|
| 8086 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=g \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.752 |
|
| 8087 |
\begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.752 |
|
| 8088 |
\begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (2 x +4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.752 |
|
| 8089 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}+5 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-6 x_{1}-6 x_{2}-5 x_{3} \\
x_{3}^{\prime }&=6 x_{1}+6 x_{2}+5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| 8090 |
\begin{align*}
8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| 8091 |
\begin{align*}
y^{\prime }&=y^{3}+{\mathrm e}^{-5 t} \\
y \left (0\right ) &= {\frac {2}{5}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.753 |
|
| 8092 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\frac {1}{x} \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.753 |
|
| 8093 |
\begin{align*}
y^{\prime \prime }-\sin \left (x \right ) y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| 8094 |
\begin{align*}
y_{1}^{\prime }&=-y_{1}+y_{2} \\
y_{2}^{\prime }&=y_{1}-y_{2}-2 y_{3} \\
y_{3}^{\prime }&=-y_{1}-y_{2}-y_{3} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 6 \\
y_{2} \left (0\right ) &= 5 \\
y_{3} \left (0\right ) &= -7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| 8095 |
\begin{align*}
x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }-y^{\prime } x +4 y&=\sin \left (\ln \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| 8096 |
\begin{align*}
\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| 8097 |
\begin{align*}
x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| 8098 |
\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*} |
✓ |
✓ |
✓ |
✗ |
0.754 |
|
| 8099 |
\begin{align*}
z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| 8100 |
\begin{align*}
8 x^{2} y^{\prime \prime }+10 y^{\prime } x +\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.754 |
|