| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 13301 |
\begin{align*}
x^{2} \left (-y^{\prime } x +y\right )&=y {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.211 |
|
| 13302 |
\begin{align*}
2 y^{\prime \prime } x +\left (-x +3\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.212 |
|
| 13303 |
\begin{align*}
t y^{\prime \prime }-y^{\prime }&=2 t^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.212 |
|
| 13304 |
\begin{align*}
\left (x +1\right ) y^{\prime \prime }+3 y^{\prime }-2 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.212 |
|
| 13305 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }-y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.212 |
|
| 13306 |
\begin{align*}
2 \sin \left (t \right ) y^{\prime \prime }+\left (1-t \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
1.213 |
|
| 13307 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x -\frac {3}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.213 |
|
| 13308 |
\begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.213 |
|
| 13309 |
\begin{align*}
x \left (x -2\right )^{2} y^{\prime \prime }-2 \left (x -2\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.213 |
|
| 13310 |
\begin{align*}
y^{\prime \prime }+\lambda ^{2} y&=0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.213 |
|
| 13311 |
\begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )&=r^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.213 |
|
| 13312 |
\begin{align*}
y^{\prime \prime }-9 y&={\mathrm e}^{3 x}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.214 |
|
| 13313 |
\begin{align*}
y y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.214 |
|
| 13314 |
\begin{align*}
\left (4 a^{2} x^{2}+1\right ) y+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.214 |
|
| 13315 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.214 |
|
| 13316 |
\begin{align*}
y^{\prime }&=\sqrt {y \left (1-y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.214 |
|
| 13317 |
\begin{align*}
y^{\prime }&=\sin \left (x -y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.215 |
|
| 13318 |
\begin{align*}
2 y^{\prime \prime \prime } y^{\prime }&=2 {y^{\prime \prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.215 |
|
| 13319 |
\begin{align*}
y^{\prime \prime } x +\left (-x +2\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.215 |
|
| 13320 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.215 |
|
| 13321 |
\begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
1.215 |
|
| 13322 |
\begin{align*}
\sqrt {x}\, y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.215 |
|
| 13323 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+x&=0 \\
y \left (2\right ) &= -1 \\
y^{\prime }\left (2\right ) &= -{\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.215 |
|
| 13324 |
\begin{align*}
y^{\prime }-3 y&=13 \cos \left (2 t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.216 |
|
| 13325 |
\begin{align*}
y^{\prime \prime }-y&=2 t^{2}+2 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.216 |
|
| 13326 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.217 |
|
| 13327 |
\begin{align*}
2 y y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.217 |
|
| 13328 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }-y x -{\mathrm e}^{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.217 |
|
| 13329 |
\begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.218 |
|
| 13330 |
\begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.218 |
|
| 13331 |
\begin{align*}
x^{\prime \prime }+x^{\prime }-2 x&=12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.218 |
|
| 13332 |
\begin{align*}
y&=x {y^{\prime }}^{2}+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.219 |
|
| 13333 |
\begin{align*}
2 x^{\prime }+y^{\prime }-3 x-y&=t \\
x^{\prime }+y^{\prime }-4 x-y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.219 |
|
| 13334 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+2 x_{2}+x_{3} \\
x_{2}^{\prime }&=-2 x_{1}+2 x_{2}+2 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-3 x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.219 |
|
| 13335 |
\begin{align*}
x^{2} y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.219 |
|
| 13336 |
\begin{align*}
y^{\prime \prime } x -2 \left (x +1\right ) y^{\prime }+2 y&=0 \\
y \left (3\right ) &= 2 \\
y^{\prime }\left (3\right ) &= 0 \\
\end{align*} Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
1.219 |
|
| 13337 |
\begin{align*}
y^{\prime \prime }-y^{\prime }&={\mathrm e}^{2 x} \sin \left ({\mathrm e}^{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.219 |
|
| 13338 |
\begin{align*}
y^{\prime }+2 y&=\operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \\
y \left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| 13339 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }&=2 \,{\mathrm e}^{2 x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| 13340 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-v^{2}+x^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| 13341 |
\begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=3 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}-\sin \left (x \right ) \\
y \left (0\right ) &= {\frac {33}{40}} \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| 13342 |
\begin{align*}
4 y+y^{\prime \prime }&=4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| 13343 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -15 y&={\mathrm e}^{x} x^{4} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| 13344 |
\begin{align*}
x^{\prime }&=-5 x+3 y+{\mathrm e}^{-t} \\
y^{\prime }&=2 x-10 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.221 |
|
| 13345 |
\begin{align*}
y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y&=f \left (t \right ) \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.221 |
|
| 13346 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +y&=2 x \,{\mathrm e}^{x}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.222 |
|
| 13347 |
\begin{align*}
x^{2} \left (2 x +1\right ) y^{\prime \prime }+2 x \left (1+6 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.222 |
|
| 13348 |
\begin{align*}
x^{\prime }+3 x-2 y&={\mathrm e}^{-t} \\
y^{\prime }-x+4 y&=\sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.222 |
|
| 13349 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=8 \,{\mathrm e}^{t}+5 t \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.222 |
|
| 13350 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.223 |
|
| 13351 |
\begin{align*}
-6+x y \left (12+3 y x -2 y^{2} x^{2}\right )+x^{2} \left (9+2 y x \right ) y^{\prime }+2 x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.223 |
|
| 13352 |
\begin{align*}
x^{4} y^{\prime \prime }&=-4 y^{2}+x^{2} y^{\prime } \left (x +y^{\prime }\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.223 |
|
| 13353 |
\begin{align*}
x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.223 |
|
| 13354 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +3 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✗ |
1.223 |
|
| 13355 |
\begin{align*}
-6 y x -y^{\prime }+x \left (x^{2}+2\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.224 |
|
| 13356 |
\begin{align*}
\left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.224 |
|
| 13357 |
\begin{align*}
1+{y^{\prime }}^{2}&=\frac {1}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.224 |
|
| 13358 |
\begin{align*}
2 y^{\prime \prime } x -y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.225 |
|
| 13359 |
\begin{align*}
\left (1+z^{\prime }\right ) {\mathrm e}^{-z}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.225 |
|
| 13360 |
\begin{align*}
t^{2} s^{\prime \prime }-t s^{\prime }&=1-\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.225 |
|
| 13361 |
\begin{align*}
2 f \left (x \right )^{2} y^{\prime \prime }&=2 f \left (x \right )^{2} y^{3}+f \left (x \right ) y^{2} f^{\prime }\left (x \right )+f \left (x \right ) \left (-2 f \left (x \right ) y+3 f^{\prime }\left (x \right )\right ) y^{\prime }+y \left (-2 f \left (x \right )^{3}-2 {f^{\prime }\left (x \right )}^{2}+f \left (x \right ) f^{\prime \prime }\left (x \right )\right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
1.226 |
|
| 13362 |
\begin{align*}
x \left (-y x +1\right ) y^{\prime }+\left (y x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.226 |
|
| 13363 |
\begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.226 |
|
| 13364 |
\begin{align*}
x^{\prime }-2 x+y^{\prime }-2 y&=1 \\
y^{\prime }+z^{\prime }+z&=2 \\
3 x+z^{\prime }+z&=3 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.226 |
|
| 13365 |
\begin{align*}
x^{\prime }&=-10 x+y+7 z \\
y^{\prime }&=-9 x+4 y+5 z \\
z^{\prime }&=-17 x+y+12 z \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 6 \\
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.226 |
|
| 13366 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.226 |
|
| 13367 |
\begin{align*}
x^{\prime }&=x+y+{\mathrm e}^{t} \\
y^{\prime }&=x-y-{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.227 |
|
| 13368 |
\begin{align*}
\left (2 x^{2}-3\right ) y^{\prime \prime }-2 y^{\prime } x +y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.227 |
|
| 13369 |
\begin{align*}
y^{\prime \prime }+\alpha y^{\prime }&=0 \\
y \left (0\right ) &= {\mathrm e}^{\alpha } \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.227 |
|
| 13370 |
\begin{align*}
x^{\prime }&=\lambda x-x^{3}-x^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.227 |
|
| 13371 |
\begin{align*}
y^{\prime }-3 y&=6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.227 |
|
| 13372 |
\begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.228 |
|
| 13373 |
\begin{align*}
x_{1}^{\prime }&=7 x_{1}-x_{4} \\
x_{2}^{\prime }&=6 x_{2} \\
x_{3}^{\prime }&=-x_{3} \\
x_{4}^{\prime }&=2 x_{1}+5 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.228 |
|
| 13374 |
\begin{align*}
4 x^{2} {y^{\prime }}^{2}-y^{2}&=x y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.228 |
|
| 13375 |
\begin{align*}
x^{\prime \prime }+4 x&=5 \sin \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.229 |
|
| 13376 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2}+3 x_{3}+4 x_{4} \\
x_{2}^{\prime }&=4 x_{1}+3 x_{2}+2 x_{3}+x_{4} \\
x_{3}^{\prime }&=4 x_{1}+5 x_{2}+6 x_{3}+7 x_{4} \\
x_{4}^{\prime }&=7 x_{1}+6 x_{2}+5 x_{3}+4 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.229 |
|
| 13377 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.229 |
|
| 13378 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (6 x^{2}-3 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.229 |
|
| 13379 |
\begin{align*}
y&=y^{\prime } x -{y^{\prime }}^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.230 |
|
| 13380 |
\begin{align*}
2 x^{\prime }+y^{\prime }-x-y&=1 \\
x^{\prime }+y^{\prime }+2 x-y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.230 |
|
| 13381 |
\begin{align*}
x^{\prime }&=5 x+2 y+5 t \\
y^{\prime }&=3 x+4 y+17 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.230 |
|
| 13382 |
\begin{align*}
y^{\prime }+\frac {4 y}{3}&=1-\frac {t}{4} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.230 |
|
| 13383 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.230 |
|
| 13384 |
\begin{align*}
y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.231 |
|
| 13385 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.231 |
|
| 13386 |
\begin{align*}
2 y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.231 |
|
| 13387 |
\begin{align*}
x^{2} y^{\prime }+y-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.231 |
|
| 13388 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.231 |
|
| 13389 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.231 |
|
| 13390 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.232 |
|
| 13391 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.232 |
|
| 13392 |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (-6\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.232 |
|
| 13393 |
\begin{align*}
y^{\prime \prime }+y&=\delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
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✓ |
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✓ |
1.232 |
|
| 13394 |
\begin{align*}
\cos \left (x \right ) y^{\prime }-\sin \left (x \right )&=0 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
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✓ |
1.232 |
|
| 13395 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }-3 y&=\cos \left ({\mathrm e}^{-x}\right ) \\
\end{align*} |
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✓ |
1.232 |
|
| 13396 |
\begin{align*}
y^{\prime }+2 y^{\prime \prime \prime }+y^{\left (5\right )}&=a x +b \cos \left (x \right )+c \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
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✓ |
1.233 |
|
| 13397 |
\begin{align*}
y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. |
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✓ |
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1.233 |
|
| 13398 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=1 \\
\end{align*} Series expansion around \(x=0\). |
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✗ |
1.233 |
|
| 13399 |
\begin{align*}
\left (y^{2} x^{2}-y x -2\right ) x y^{\prime }+y \left (y^{2} x^{2}-1\right )&=0 \\
\end{align*} |
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1.233 |
|
| 13400 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +p^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
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✓ |
1.233 |
|