| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 24201 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=-32 t^{2} \cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
42.973 |
|
| 24202 |
\begin{align*}
y^{\prime }&=\frac {y}{\sqrt {t^{3}-3}}+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
42.987 |
|
| 24203 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=x \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
42.990 |
|
| 24204 |
\begin{align*}
p \left (2 k +p \right ) y-\left (1+2 k \right ) x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
42.997 |
|
| 24205 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=10 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.000 |
|
| 24206 |
\begin{align*}
y^{\prime }&=\frac {6 x^{2} y-2 x +1-5 x^{3} y^{2}-2 y x +y^{3} x^{4}}{x^{2} \left (x^{2} y-x +1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
43.042 |
|
| 24207 |
\begin{align*}
x^{\prime \prime }-x^{\prime }+x&=\sin \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.067 |
|
| 24208 |
\begin{align*}
y^{\prime }&=y^{2}-2 a b \cot \left (a x \right ) y+b^{2}-a^{2} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
43.068 |
|
| 24209 |
\begin{align*}
m y^{\prime \prime }+k \sin \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
43.074 |
|
| 24210 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{3 x} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.089 |
|
| 24211 |
\begin{align*}
y^{\prime }&=\left (1+y^{2}\right ) \sqrt {1+\cos \left (x^{3}\right )} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
43.122 |
|
| 24212 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.132 |
|
| 24213 |
\begin{align*}
y-\left (x +1\right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
43.168 |
|
| 24214 |
\begin{align*}
y^{\prime } x&=\lambda \arcsin \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arcsin \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
43.177 |
|
| 24215 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }-5 y&=-648 t^{2} {\mathrm e}^{5 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.195 |
|
| 24216 |
\begin{align*}
3 x -y-6+\left (x +y+2\right ) y^{\prime }&=0 \\
y \left (2\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.209 |
|
| 24217 |
\begin{align*}
\left (5 x +y-7\right ) y^{\prime }&=3 x +3 y+3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.211 |
|
| 24218 |
\begin{align*}
y y^{\prime }-y&=\frac {4}{9} x +2 A \,x^{2}+2 A^{2} x^{3} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
43.268 |
|
| 24219 |
\begin{align*}
y-\left (x +\sqrt {y^{2}-x^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.273 |
|
| 24220 |
\begin{align*}
y^{\prime \prime }+3 y&=t \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.299 |
|
| 24221 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=2 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.355 |
|
| 24222 |
\begin{align*}
y^{\prime }&=\frac {2 a x +2 a +x^{3} \sqrt {-y^{2}+4 a x}}{\left (x +1\right ) y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
43.423 |
|
| 24223 |
\begin{align*}
y^{\prime } y^{2} x +y^{3}&=\cos \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.429 |
|
| 24224 |
\begin{align*}
\left (2+x \right ) y^{\prime \prime }-y^{\prime }+\frac {y}{2+x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.443 |
|
| 24225 |
\begin{align*}
y^{\prime }&=\frac {x}{2}+\frac {1}{2}+\sqrt {x^{2}+2 x +1-4 y}+x^{2} \sqrt {x^{2}+2 x +1-4 y}+x^{3} \sqrt {x^{2}+2 x +1-4 y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
43.459 |
|
| 24226 |
\begin{align*}
y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+\lambda \arctan \left (x \right )^{n} \left (x^{1+k} y-1\right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
43.483 |
|
| 24227 |
\begin{align*}
x \left (a \,x^{k}+b \right ) y^{\prime }&=\alpha \,x^{n} y^{2}+\left (\beta -a n \,x^{k}\right ) y+\gamma \,x^{-n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
43.566 |
|
| 24228 |
\begin{align*}
\left (a \,x^{2}+b x +c \right )^{{3}/{2}} y^{\prime \prime }-F \left (\frac {y}{\sqrt {a \,x^{2}+b x +c}}\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
43.652 |
|
| 24229 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda x \arcsin \left (x \right )^{n} y+\arcsin \left (x \right )^{n} \lambda \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
43.708 |
|
| 24230 |
\begin{align*}
y^{\prime }&=\frac {y^{3} x \,{\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{9 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+3 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+9 y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
43.714 |
|
| 24231 |
\begin{align*}
2 x \sin \left (\frac {y}{x}\right )+2 x \tan \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )-y \sec \left (\frac {y}{x}\right )^{2}+\left (x \cos \left (\frac {y}{x}\right )+x \sec \left (\frac {y}{x}\right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
43.730 |
|
| 24232 |
\begin{align*}
y^{\prime }&=\frac {y \left (x -y\right ) \left (1+y\right )}{x \left (y x +x -y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
43.804 |
|
| 24233 |
\begin{align*}
\left (y^{\prime } x +y\right )^{2}&=y^{2} y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.823 |
|
| 24234 |
\begin{align*}
x \left (4 x -y\right ) y^{\prime }+4 x^{2}-6 y x -y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.850 |
|
| 24235 |
\begin{align*}
x \cos \left (y\right )^{2}+\tan \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.882 |
|
| 24236 |
\begin{align*}
x^{2} {y^{\prime }}^{3}+\left (2 x +y\right ) y y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
43.895 |
|
| 24237 |
\begin{align*}
4 y+y^{\prime \prime }&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.913 |
|
| 24238 |
\begin{align*}
x^{\prime \prime }+w^{2} x&=\cos \left (\beta t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.961 |
|
| 24239 |
\begin{align*}
y^{\prime \prime }-4 y&={\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
43.961 |
|
| 24240 |
\begin{align*}
x^{\prime }&=t^{2}+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
43.969 |
|
| 24241 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x +a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
43.982 |
|
| 24242 |
\begin{align*}
x^{3} y^{\prime \prime }+x^{2} y^{\prime }+\left (a \,x^{2}+b x +a \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
43.985 |
|
| 24243 |
\begin{align*}
a {y^{\prime }}^{2}+y y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
43.990 |
|
| 24244 |
\begin{align*}
\left (1-2 x +y\right ) y^{\prime }+y+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.030 |
|
| 24245 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+2 x&=t \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.051 |
|
| 24246 |
\begin{align*}
x^{3} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
44.068 |
|
| 24247 |
\begin{align*}
\left (a^{2} {\mathrm e}^{2 \lambda x}+b \right ) y^{\prime \prime }-b \lambda y^{\prime }-a^{2} \lambda ^{2} k^{2} {\mathrm e}^{2 \lambda x} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
44.083 |
|
| 24248 |
\begin{align*}
y^{\prime \prime }+9 y&=x^{3} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.168 |
|
| 24249 |
\begin{align*}
y^{\prime }-a \left (x^{n}-x \right ) y^{3}-y^{2}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
44.231 |
|
| 24250 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-8 y&=-t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.273 |
|
| 24251 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.283 |
|
| 24252 |
\begin{align*}
y^{\prime }&=\frac {\cos \left (x \right )-2 x y^{2}}{2 x^{2} y} \\
y \left (\pi \right ) &= \frac {1}{\pi } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.291 |
|
| 24253 |
\begin{align*}
x \left (x -2\right ) y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 \left (x -1\right ) y&=3 x^{2} \left (x -2\right )^{2} {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
44.304 |
|
| 24254 |
\begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=2 x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
44.325 |
|
| 24255 |
\begin{align*}
\sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime }&=0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.329 |
|
| 24256 |
\begin{align*}
y^{\prime }&=-\frac {x}{2}+1+\sqrt {x^{2}-4 x +4 y}+x^{2} \sqrt {x^{2}-4 x +4 y}+x^{3} \sqrt {x^{2}-4 x +4 y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
44.345 |
|
| 24257 |
\begin{align*}
y^{\prime \prime }+9 y&=9 x^{4}-9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.359 |
|
| 24258 |
\begin{align*}
2 x^{3} y^{\prime }&=y \left (3 x^{2}+y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.365 |
|
| 24259 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.371 |
|
| 24260 |
\begin{align*}
x +3 y-5-\left (x -y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.396 |
|
| 24261 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=6 x +4 \\
y \left (1\right ) &= 4 \\
y^{\prime }\left (1\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.457 |
|
| 24262 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{a x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.481 |
|
| 24263 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=\sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.490 |
|
| 24264 |
\begin{align*}
y^{\prime } x&=\lambda \operatorname {arccot}\left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \operatorname {arccot}\left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
44.517 |
|
| 24265 |
\begin{align*}
x^{2} \left (x y^{2}-1\right ) {y^{\prime }}^{2}+2 x^{2} y^{2} \left (-x +y\right ) y^{\prime }-y^{2} \left (x^{2} y-1\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
44.530 |
|
| 24266 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=\sin \left (x \right ) {\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.546 |
|
| 24267 |
\begin{align*}
y^{\prime }&=-\frac {2 x}{3}+\sqrt {x^{2}+3 y}+x^{2} \sqrt {x^{2}+3 y}+x^{3} \sqrt {x^{2}+3 y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
44.576 |
|
| 24268 |
\begin{align*}
\left (y+2 x -2\right ) y^{\prime }-y+x +1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.585 |
|
| 24269 |
\begin{align*}
y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+\sqrt {x^{2}-2 x +1+8 y}+x^{2} \sqrt {x^{2}-2 x +1+8 y}+x^{3} \sqrt {x^{2}-2 x +1+8 y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
44.681 |
|
| 24270 |
\begin{align*}
y^{\prime \prime }+7 y^{\prime }+12 y&=3 t^{2} {\mathrm e}^{-4 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.690 |
|
| 24271 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
y^{\prime }\left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.716 |
|
| 24272 |
\begin{align*}
y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} \cot \left (x \right )^{m} y-a \cot \left (x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
44.722 |
|
| 24273 |
\begin{align*}
x^{\prime }&=4 x^{2}+4 \\
x \left (\frac {\pi }{4}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
44.802 |
|
| 24274 |
\begin{align*}
y^{\prime }&=\frac {y \left (1+y\right )}{x \left (-y-1+y x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.877 |
|
| 24275 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=10 \sin \left (4 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
44.882 |
|
| 24276 |
\begin{align*}
-\left (2+x \right ) y-\left (-x^{2}-x +1\right ) y^{\prime }+\left (x +1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
44.968 |
|
| 24277 |
\begin{align*}
y^{\prime } \cos \left (y\right )-\cos \left (x \right ) \sin \left (y\right )^{2}-\sin \left (y\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
44.971 |
|
| 24278 |
\begin{align*}
x -2 y+1+\left (4 x -3 y-6\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
45.004 |
|
| 24279 |
\begin{align*}
y^{\prime }&=\frac {y \,{\mathrm e}^{-\frac {x^{2}}{2}} \left (2 y^{2}+2 y \,{\mathrm e}^{\frac {x^{2}}{4}}+2 \,{\mathrm e}^{\frac {x^{2}}{2}}+x \,{\mathrm e}^{\frac {x^{2}}{2}}\right )}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
45.014 |
|
| 24280 |
\begin{align*}
y^{\prime }&=\frac {y \left (x +y\right ) \left (1+y\right )}{x \left (y x +x +y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
45.042 |
|
| 24281 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=\frac {5 \ln \left (x \right )}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
45.085 |
|
| 24282 |
\begin{align*}
y^{\prime }&=\lambda \arccos \left (x \right )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \arccos \left (x \right )^{n} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
45.089 |
|
| 24283 |
\begin{align*}
y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
45.094 |
|
| 24284 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (x -1\right )}+\frac {v \left (v +1\right ) y}{4 x^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
45.119 |
|
| 24285 |
\begin{align*}
x +3 y-4+\left (x +4 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
45.130 |
|
| 24286 |
\begin{align*}
f \left (x \right )^{2} y^{\prime }-f^{\prime }\left (x \right ) y^{2}+g \left (x \right ) \left (y-f \left (x \right )\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
45.162 |
|
| 24287 |
\begin{align*}
y y^{\prime }-y&=12 x +\frac {A}{x^{{5}/{2}}} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
45.174 |
|
| 24288 |
\begin{align*}
y^{\prime }-3 y&=-10 \,{\mathrm e}^{-t +a} \sin \left (-2 t +2 a \right ) \operatorname {Heaviside}\left (t -a \right ) \\
y \left (0\right ) &= 5 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
45.180 |
|
| 24289 |
\begin{align*}
y^{\prime } y^{2} x +y^{3}&=\cos \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
45.185 |
|
| 24290 |
\begin{align*}
\left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
45.301 |
|
| 24291 |
\begin{align*}
y^{\prime }&=-y^{3} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
45.346 |
|
| 24292 |
\begin{align*}
y^{\prime }&=a \sin \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
45.369 |
|
| 24293 |
\begin{align*}
r^{\prime \prime }+2 r^{\prime }+r&=1 \\
r \left (0\right ) &= 0 \\
r^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
45.433 |
|
| 24294 |
\begin{align*}
x^{\prime }&=2+\sin \left (x\right ) \\
x \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
45.436 |
|
| 24295 |
\begin{align*}
2 y y^{\prime }&=\left (7 a x +5 b \right ) y-3 a^{2} x^{3}-2 c \,x^{2}-3 b^{2} x \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
45.455 |
|
| 24296 |
\begin{align*}
y y^{\prime }&=\left (a x +3 b \right ) y+c \,x^{3}-b \,x^{2} a -2 b^{2} x \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
45.551 |
|
| 24297 |
\begin{align*}
y^{\prime \prime }+9 y&=27 x +18 \\
y \left (0\right ) &= 23 \\
y^{\prime }\left (0\right ) &= 21 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
45.563 |
|
| 24298 |
\begin{align*}
\left (a \,x^{2}+b x \right ) y^{\prime \prime }+2 b y^{\prime }-2 a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
45.616 |
|
| 24299 |
\begin{align*}
y^{\prime }&=\frac {3 x -y+1}{2 x +y+4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
45.629 |
|
| 24300 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=2 \cos \left (t \right )^{2} {\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
45.664 |
|