| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 7201 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| 7202 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| 7203 |
\begin{align*}
x^{\prime }&=7 x+4 y-4 z \\
y^{\prime }&=4 x-8 y-z \\
z^{\prime }&=-4 x-y-8 z \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 5 \\
z \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| 7204 |
\begin{align*}
t^{2} \left (1+t \right ) y^{\prime \prime }-t \left (2 t +1\right ) y^{\prime }+\left (2 t +1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| 7205 |
\begin{align*}
z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}&=0 \\
\end{align*} Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 7206 |
\begin{align*}
x_{1}^{\prime }&=9 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=5 x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 7207 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 7208 |
\begin{align*}
y^{\prime }&=\frac {1}{-3+y} \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 7209 |
\begin{align*}
x +3 y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 7210 |
\begin{align*}
x^{\prime }-y+z&=0 \\
-x+y^{\prime }-y&=t \\
z^{\prime }-x-z&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 7211 |
\begin{align*}
y^{\prime \prime \prime \prime }-16 y&=x^{2} \sin \left (2 x \right )+x^{4} {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 7212 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 7213 |
\begin{align*}
x^{\prime }+5 x+y&={\mathrm e}^{t} \\
y^{\prime }-x+3 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| 7214 |
\begin{align*}
\left (x^{2}-x +1\right ) y^{\prime \prime }-\left (1-4 x \right ) y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 7215 |
\begin{align*}
x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 7216 |
\begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 7217 |
\begin{align*}
x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 7218 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{49}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 7219 |
\begin{align*}
y^{\prime \prime }&=2 a \left (c +b x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.631 |
|
| 7220 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\frac {2}{y}} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
0.631 |
|
| 7221 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=\tan \left (2 t \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 7222 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.631 |
|
| 7223 |
\begin{align*}
x^{\prime }&=x-y-z \\
y^{\prime }&=y+3 z \\
z^{\prime }&=3 y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| 7224 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| 7225 |
\begin{align*}
x^{2} y^{\prime \prime }+\frac {3 y^{\prime } x}{2}-\frac {\left (x +1\right ) y}{2}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| 7226 |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.632 |
|
| 7227 |
\begin{align*}
y^{\prime \prime } x +y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| 7228 |
\begin{align*}
12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.632 |
|
| 7229 |
\begin{align*}
f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.632 |
|
| 7230 |
\begin{align*}
x^{\prime }&=y+{\mathrm e}^{t} \\
y^{\prime }&=-2 x+3 y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| 7231 |
\begin{align*}
\left (x +4\right ) y^{\prime \prime }-\left (2 x +4\right ) y^{\prime }+\left (6+x \right ) y&=0 \\
y \left (-3\right ) &= 2 \\
y^{\prime }\left (-3\right ) &= -2 \\
\end{align*} Series expansion around \(x=-3\). |
✓ |
✓ |
✓ |
✓ |
0.633 |
|
| 7232 |
\begin{align*}
z y^{\prime \prime }-2 y^{\prime }+y z&=0 \\
\end{align*} Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
0.633 |
|
| 7233 |
\begin{align*}
{y^{\prime }}^{3}+a x y^{\prime }-a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.633 |
|
| 7234 |
\begin{align*}
\left (2 t +1\right ) y^{\prime \prime }-4 \left (1+t \right ) y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.633 |
|
| 7235 |
\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*} |
✓ |
✓ |
✓ |
✗ |
0.633 |
|
| 7236 |
\begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.633 |
|
| 7237 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| 7238 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| 7239 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x^{3}-x \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.634 |
|
| 7240 |
\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*} |
✓ |
✓ |
✓ |
✗ |
0.634 |
|
| 7241 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| 7242 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| 7243 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| 7244 |
\begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| 7245 |
\begin{align*}
x_{1}^{\prime }&=147 x_{1}+23 x_{2}-202 x_{3} \\
x_{2}^{\prime }&=-90 x_{1}-9 x_{2}+129 x_{3} \\
x_{3}^{\prime }&=90 x_{1}+15 x_{2}-123 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| 7246 |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+18 y^{\prime }&=-{\mathrm e}^{3 x} \left (\left (2-3 x \right ) \cos \left (3 x \right )-\left (3 x +3\right ) \sin \left (3 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| 7247 |
\begin{align*}
t^{2} y^{\prime \prime }-y^{\prime } t -\left (t^{2}+\frac {5}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| 7248 |
\begin{align*}
y x -1+\left (x^{2}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.635 |
|
| 7249 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime } x -y&=x \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.635 |
|
| 7250 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.635 |
|
| 7251 |
\begin{align*}
9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.635 |
|
| 7252 |
\begin{align*}
y^{\prime }&=-\frac {i \left (i x +x^{4}+2 y^{2} x^{2}+y^{4}\right )}{y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.635 |
|
| 7253 |
\begin{align*}
t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| 7254 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.636 |
|
| 7255 |
\begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.636 |
|
| 7256 |
\begin{align*}
2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| 7257 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| 7258 |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=x_{3} \\
x_{3}^{\prime }&=6 t \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| 7259 |
\begin{align*}
y_{1}^{\prime }&=-y_{1}-4 y_{2}+4 \\
y_{2}^{\prime }&=y_{1}-y_{2}+1 \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| 7260 |
\begin{align*}
2 y^{\prime \prime } x -\left (2 x +3\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.637 |
|
| 7261 |
\begin{align*}
x^{\prime }&=-3 x-3 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.637 |
|
| 7262 |
\begin{align*}
{x^{\prime }}^{2}&=-4 x+4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.637 |
|
| 7263 |
\begin{align*}
y^{\prime }-4 y&=\delta \left (t -4\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.637 |
|
| 7264 |
\begin{align*}
\left ({\mathrm e}^{2 y}+x \right ) {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.638 |
|
| 7265 |
\begin{align*}
16 x^{2} y^{\prime \prime }+16 y^{\prime } x +\left (16 x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 7266 |
\begin{align*}
9 x^{2} y^{\prime \prime }+9 y^{\prime } x +\left (x^{6}-36\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 7267 |
\begin{align*}
y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.638 |
|
| 7268 |
\begin{align*}
a \,x^{2} y y^{\prime \prime }+b \,x^{2} {y^{\prime }}^{2}+c x y y^{\prime }+d y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.638 |
|
| 7269 |
\begin{align*}
4 x^{\prime }+9 y^{\prime }+11 x+31 y&={\mathrm e}^{t} \\
3 x^{\prime }+7 y^{\prime }+8 x+24 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 7270 |
\begin{align*}
2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 7271 |
\begin{align*}
y&=y^{\prime } x +k {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 7272 |
\begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| 7273 |
\begin{align*}
4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| 7274 |
\begin{align*}
4 y^{\prime \prime } x +3 y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| 7275 |
\begin{align*}
2 y&={y^{\prime }}^{2}+4 y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.639 |
|
| 7276 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| 7277 |
\begin{align*}
x^{\prime }&=8 x-5 y \\
y^{\prime }&=16 x+8 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| 7278 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\
x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| 7279 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| 7280 |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| 7281 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| 7282 |
\begin{align*}
x y y^{\prime \prime }&=y^{\prime }+{y^{\prime }}^{3} \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
0.640 |
|
| 7283 |
\begin{align*}
y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| 7284 |
\begin{align*}
2 y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| 7285 |
\begin{align*}
x^{2}&=a^{2} \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| 7286 |
\begin{align*}
x_{1}^{\prime }&=-\frac {x_{1}}{4}+x_{2} \\
x_{2}^{\prime }&=-x_{1}-\frac {x_{2}}{4} \\
x_{3}^{\prime }&=\frac {x_{3}}{10} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| 7287 |
\begin{align*}
16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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0.641 |
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| 7288 |
\begin{align*}
y^{\prime \prime }-{\mathrm e}^{x} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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0.641 |
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| 7289 |
\begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=5 x+2 y \\
\end{align*} |
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0.641 |
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| 7290 |
\begin{align*}
2 y^{\prime \prime } x +5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\
\end{align*} |
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0.641 |
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| 7291 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\
\end{align*} |
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| 7292 |
\begin{align*}
y^{\prime }&=\tan \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
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0.641 |
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| 7293 |
\begin{align*}
x^{\prime }&=-3 x+2 \pi y \\
y^{\prime }&=4 x-y \\
\end{align*} |
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| 7294 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+35 \,{\mathrm e}^{t} t^{{3}/{2}} \\
\end{align*} |
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0.642 |
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| 7295 |
\begin{align*}
y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
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| 7296 |
\begin{align*}
4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y&=0 \\
\end{align*} |
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0.642 |
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| 7297 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
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0.642 |
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| 7298 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
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| 7299 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }&=\left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \\
y \left (0\right ) &= -6 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
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| 7300 |
\begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=-3 x+4 y \\
\end{align*} |
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0.642 |
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