| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 4201 |
\begin{align*}
x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| 4202 |
\begin{align*}
y y^{\prime }&=1-x {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.329 |
|
| 4203 |
\begin{align*}
x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.329 |
|
| 4204 |
\begin{align*}
x^{\prime }&=x-3 y \\
y^{\prime }&=3 x+7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| 4205 |
\begin{align*}
x^{\prime }&=-6 x+2 y \\
y^{\prime }&=-2 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| 4206 |
\begin{align*}
y^{\prime }&=\frac {1}{x -1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| 4207 |
\begin{align*}
y^{\prime }&=\sin \left (\frac {x}{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| 4208 |
\begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=3 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| 4209 |
\begin{align*}
x^{\prime }&=-\frac {3 x}{4}-\frac {7 y}{4} \\
y^{\prime }&=\frac {x}{4}+\frac {5 y}{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| 4210 |
\begin{align*}
x^{\prime }&=-\frac {x}{4}-\frac {3 y}{4} \\
y^{\prime }&=\frac {x}{2}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| 4211 |
\begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| 4212 |
\begin{align*}
\left (1+{y^{\prime }}^{2}\right ) x&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| 4213 |
\begin{align*}
y^{\prime }&=2 y x -x^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| 4214 |
\begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| 4215 |
\begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| 4216 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| 4217 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| 4218 |
\begin{align*}
x_{1}^{\prime }&=-50 x_{1}+20 x_{2} \\
x_{2}^{\prime }&=100 x_{1}-60 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.330 |
|
| 4219 |
\begin{align*}
y^{\prime \prime }+k^{2} x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.330 |
|
| 4220 |
\begin{align*}
y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.330 |
|
| 4221 |
\begin{align*}
2 y y^{\prime \prime }&=-1-2 x y^{2}+a y^{3}+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.330 |
|
| 4222 |
\begin{align*}
6 y^{\prime \prime } x +6 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.330 |
|
| 4223 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.330 |
|
| 4224 |
\begin{align*}
b x +a y {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.330 |
|
| 4225 |
\begin{align*}
x^{\prime }&=-6 y \\
y^{\prime }&=6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.330 |
|
| 4226 |
\begin{align*}
x^{\prime }&=\cos \left (t \right ) \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.330 |
|
| 4227 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 y^{\prime } x&=\ln \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.330 |
|
| 4228 |
\begin{align*}
{y^{\prime }}^{2}+y^{\prime } x +y y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.330 |
|
| 4229 |
\begin{align*}
y_{1}^{\prime }&=2 y_{1}+y_{2} \\
y_{2}^{\prime }&=2 y_{2} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -1 \\
y_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.330 |
|
| 4230 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| 4231 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+9 x_{2} \\
x_{2}^{\prime }&=-x_{1}-3 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| 4232 |
\begin{align*}
y^{\prime \prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| 4233 |
\begin{align*}
3 y+y^{\prime }&=2 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| 4234 |
\begin{align*}
y^{\prime \prime }-2 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| 4235 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| 4236 |
\begin{align*}
2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.331 |
|
| 4237 |
\begin{align*}
x^{\prime }&=-2 x \\
y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| 4238 |
\begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+3 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| 4239 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| 4240 |
\begin{align*}
x \left (1-3 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+9 x^{2} \ln \left (x \right )\right ) y^{\prime }-\left (3+9 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.331 |
|
| 4241 |
\begin{align*}
y^{\prime \prime }-y x&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| 4242 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| 4243 |
\begin{align*}
y^{\prime \prime \prime }-4 y^{\prime }&=t +\cos \left (t \right )+2 \,{\mathrm e}^{-2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| 4244 |
\begin{align*}
y^{2} {y^{\prime }}^{2}+2 y y^{\prime } x +x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| 4245 |
\begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2}-4 y^{2} \left (x +2 y\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.332 |
|
| 4246 |
\begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=-5 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| 4247 |
\begin{align*}
y_{1}^{\prime }&=2 y_{1}-3 y_{2} \\
y_{2}^{\prime }&=y_{1}-2 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| 4248 |
\begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| 4249 |
\begin{align*}
y_{1}^{\prime }&=5 y_{1}-y_{2}+{\mathrm e}^{-t} \\
y_{2}^{\prime }&=y_{1}+3 y_{2}+2 \,{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -3 \\
y_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| 4250 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| 4251 |
\begin{align*}
x^{\prime }-2 y^{\prime }&={\mathrm e}^{t} \\
x^{\prime }+y^{\prime }&=\sqrt {t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| 4252 |
\begin{align*}
x^{\prime }&=5 x-6 y \\
y^{\prime }&=6 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| 4253 |
\begin{align*}
y^{\prime }&=2 y \\
y \left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| 4254 |
\begin{align*}
y^{\prime \prime }+k^{2} y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| 4255 |
\begin{align*}
y^{\prime }&=\sin \left (5 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| 4256 |
\begin{align*}
\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \\
y \left (-3\right ) &= 1 \\
y^{\prime }\left (-3\right ) &= 0 \\
\end{align*} Series expansion around \(x=-3\). |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| 4257 |
\begin{align*}
4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| 4258 |
\begin{align*}
y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+2 y&=8 x^{2} {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.333 |
|
| 4259 |
\begin{align*}
5 x^{5} y^{\prime \prime \prime \prime }+4 x^{4} y^{\prime \prime \prime }+x^{2} y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| 4260 |
\begin{align*}
y^{\prime } t +y&=0 \\
y \left (0\right ) &= y_{0} \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✗ |
✓ |
0.333 |
|
| 4261 |
\begin{align*}
2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.333 |
|
| 4262 |
\begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+y&={\mathrm e}^{-\frac {t}{2}} \delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| 4263 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{-3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| 4264 |
\begin{align*}
y^{\prime \prime }-12 y^{\prime }+45 y&=\delta \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| 4265 |
\begin{align*}
2 x -1-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| 4266 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=4 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| 4267 |
\begin{align*}
y_{1}^{\prime }&=4 y_{1}-4 y_{2} \\
y_{2}^{\prime }&=5 y_{1}-4 y_{2} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| 4268 |
\begin{align*}
x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=\ln \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| 4269 |
\begin{align*}
y^{\prime }-y&=x^{2}+1 \\
y \left (0\right ) &= -3 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| 4270 |
\begin{align*}
x_{1}^{\prime }&=-4 x_{1} \\
x_{2}^{\prime }&=-4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.334 |
|
| 4271 |
\begin{align*}
x \left (-y x +1\right ) \left (1-y^{2} x^{2}\right ) y^{\prime }+\left (y x +1\right ) \left (1+y^{2} x^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.334 |
|
| 4272 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.334 |
|
| 4273 |
\begin{align*}
-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.334 |
|
| 4274 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.334 |
|
| 4275 |
\begin{align*}
x^{\prime }&=7 x-4 y \\
y^{\prime }&=x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.334 |
|
| 4276 |
\begin{align*}
y_{1}^{\prime }&=6 y_{2} \\
y_{2}^{\prime }&=-6 y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 5 \\
y_{2} \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.334 |
|
| 4277 |
\begin{align*}
{y^{\prime }}^{3}-\left (y+2 x -{\mathrm e}^{x -y}\right ) {y^{\prime }}^{2}+\left (2 y x -2 x \,{\mathrm e}^{x -y}-y \,{\mathrm e}^{x -y}\right ) y^{\prime }+2 x y \,{\mathrm e}^{x -y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.334 |
|
| 4278 |
\begin{align*}
\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 y y^{\prime } x +y^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.334 |
|
| 4279 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.334 |
|
| 4280 |
\begin{align*}
x^{3} y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.334 |
|
| 4281 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }-4 y&=25 t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.334 |
|
| 4282 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| 4283 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=9 x^{2} \\
y \left (1\right ) &= -7 \\
y^{\prime }\left (1\right ) &= -11 \\
y^{\prime \prime }\left (1\right ) &= -5 \\
y^{\prime \prime \prime }\left (1\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| 4284 |
\begin{align*}
\left (1-t \right ) y^{\prime \prime }+y^{\prime } t +y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| 4285 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=4 \,{\mathrm e}^{2 x} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| 4286 |
\begin{align*}
{y^{\prime }}^{2}+a \,x^{3} y^{\prime }-2 a \,x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| 4287 |
\begin{align*}
\sin \left (y^{\prime }\right )+y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.335 |
|
| 4288 |
\begin{align*}
y^{\prime \prime }+k^{2} x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| 4289 |
\begin{align*}
y^{\prime }&=x \,{\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| 4290 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| 4291 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.335 |
|
| 4292 |
\begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=x-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| 4293 |
\begin{align*}
y^{\prime \prime }+4 y&=t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| 4294 |
\begin{align*}
x^{\prime }&=5 x-y \\
y^{\prime }&=3 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| 4295 |
\begin{align*}
x^{\prime }&=-3 x+4 y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| 4296 |
\begin{align*}
y^{\prime \prime } x +y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| 4297 |
\begin{align*}
y^{\prime \prime }+13 y^{\prime }+36 y&=10-72 t \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| 4298 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-15 y&=16 t \,{\mathrm e}^{-t}-15 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -9 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| 4299 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| 4300 |
\begin{align*}
y^{\prime \prime }+x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.336 |
|