| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12301 |
\begin{align*}
x^{\prime \prime }-x&={\mathrm e}^{t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 12302 |
\begin{align*}
4 {y^{\prime }}^{2} x \left (x -a \right ) \left (-b +x \right )&=\left (3 x^{2}-2 \left (a +b \right ) x +a b \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 12303 |
\begin{align*}
\sqrt {x}\, y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 12304 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 12305 |
\begin{align*}
y^{\prime \prime \prime }-y&=3 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| 12306 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (t \right ) \cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| 12307 |
\begin{align*}
x^{\prime }-4 x+3 y&=\sin \left (t \right ) \\
-2 x+y^{\prime }+y&=-2 \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| 12308 |
\begin{align*}
y^{\prime }&=\sin \left (x \right ) \left (2 \sec \left (x \right )^{2}-y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.703 |
|
| 12309 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| 12310 |
\begin{align*}
y^{\prime \prime }+\sin \left (y\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.703 |
|
| 12311 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| 12312 |
\begin{align*}
y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \cos \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| 12313 |
\begin{align*}
x^{\prime \prime }+{x^{\prime }}^{2}+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.703 |
|
| 12314 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+8 y&={\mathrm e}^{x}+{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| 12315 |
\begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| 12316 |
\begin{align*}
y&=-y^{\prime } x +x^{4} {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| 12317 |
\begin{align*}
y^{\prime \prime }+a_{1} \left (t \right ) y^{\prime }+a_{0} \left (t \right ) y&=f \left (t \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.703 |
|
| 12318 | \begin{align*}
3 y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. | ✓ | ✗ | ✓ | ✗ | 0.703 |
|
| 12319 |
\begin{align*}
y^{\prime \prime }-y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| 12320 |
\begin{align*}
t^{2} y^{\prime \prime }+t \,{\mathrm e}^{t} y^{\prime }+4 \left (1-4 t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.703 |
|
| 12321 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (a x \right ) \sin \left (b x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.704 |
|
| 12322 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 12323 |
\begin{align*}
9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 12324 |
\begin{align*}
{y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 12325 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.704 |
|
| 12326 |
\begin{align*}
3 x^{\prime }+2 y^{\prime }&=\sin \left (t \right ) \\
x^{\prime }-2 y^{\prime }&=x+y+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 12327 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=10 x^{3} {\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 12328 |
\begin{align*}
x {y^{\prime }}^{2}-2 y^{\prime } y+a x&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
0.704 |
|
| 12329 |
\begin{align*}
x^{\prime \prime }+x&=0 \\
x \left (\frac {\pi }{6}\right ) &= {\frac {1}{2}} \\
x^{\prime }\left (\frac {\pi }{6}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| 12330 |
\begin{align*}
2 y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 12331 |
\begin{align*}
2 y^{\prime \prime }-3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 12332 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 12333 |
\begin{align*}
y+\left (3 x +2\right ) y^{\prime }+x \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.705 |
|
| 12334 |
\begin{align*}
y^{\prime \prime } x +\left (\frac {1}{2}-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 12335 |
\begin{align*}
y&=\left (x +1\right ) {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 12336 |
\begin{align*}
2 x^{\prime }+4 y^{\prime }+x-y&=3 \,{\mathrm e}^{t} \\
x^{\prime }+y^{\prime }+2 x+2 y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 12337 | \begin{align*}
y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.705 |
|
| 12338 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 x}}{x^{4}} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= {\mathrm e}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| 12339 |
\begin{align*}
2 {y^{\prime }}^{3}-3 {y^{\prime }}^{2}+x&=y \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.706 |
|
| 12340 |
\begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}&=b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 12341 |
\begin{align*}
y^{\prime \prime } x +\frac {y^{\prime }}{2}+\frac {y}{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 12342 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 12343 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| 12344 |
\begin{align*}
\left (x -a \right ) \left (-b +x \right ) y^{\prime \prime }+2 \left (2 x -a -b \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.706 |
|
| 12345 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 12346 |
\begin{align*}
y^{\prime \prime }-\frac {\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right )}{x \left (-x^{2}+2\right )}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 12347 |
\begin{align*}
\left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y+a y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.707 |
|
| 12348 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 12349 |
\begin{align*}
\left (y^{2}+x^{2}\right )^{2} {y^{\prime }}^{2}&=4 y^{2} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.707 |
|
| 12350 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x -x^{3}+2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.707 |
|
| 12351 |
\begin{align*}
x^{\prime }&=2 x+2 y \\
y^{\prime }&=6 x+3 y+{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 12352 |
\begin{align*}
\cos \left (x \right ) y^{\prime }-\sin \left (x \right )&=0 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 12353 |
\begin{align*}
y^{\prime }&=y^{3}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 12354 |
\begin{align*}
y^{\prime \prime }+9 y&=\sin \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 12355 |
\begin{align*}
y \left (1+{y^{\prime }}^{2}\right )&=2 \alpha \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 12356 |
\begin{align*}
a {y^{\prime }}^{3}&=27 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| 12357 | \begin{align*}
y^{\prime }-y^{\prime \prime } x -\frac {a^{2} y^{\prime }}{x}+\frac {x^{2}}{a}&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.707 |
|
| 12358 |
\begin{align*}
y^{\prime } x +\left (2 x -3\right ) y&=4 x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 12359 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right )^{3} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 12360 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=\left (3 t^{7}-5 t^{4}\right ) {\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 12361 |
\begin{align*}
y^{\prime \prime }+y&=x^{3}-1+2 \cos \left (x \right )+\left (2-4 x \right ) {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 12362 |
\begin{align*}
y^{\prime \prime } x -\left (x -1\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 12363 |
\begin{align*}
y^{\prime \prime }-x^{2} y-x^{4}+2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.708 |
|
| 12364 |
\begin{align*}
y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y-\cosh \left (a x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 12365 |
\begin{align*}
y^{\prime \prime }+16 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 12366 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\frac {y^{\prime }}{y}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.708 |
|
| 12367 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.708 |
|
| 12368 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }-y&=\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 12369 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 12370 |
\begin{align*}
x^{\prime }&=5 x+3 y+1 \\
y^{\prime }&=-6 x-4 y+{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 12371 |
\begin{align*}
x^{\prime }&=2 x+6 y+{\mathrm e}^{t} \\
y^{\prime }&=x+3 y-{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| 12372 |
\begin{align*}
x \left (x^{2}+x +3\right ) y^{\prime \prime }+\left (-x^{2}+x +4\right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| 12373 |
\begin{align*}
-12 y-2 \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.709 |
|
| 12374 |
\begin{align*}
x^{\prime }+y-t^{2}+6 t +1&=0 \\
-x+y^{\prime }&=-3 t^{2}+3 t +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| 12375 |
\begin{align*}
{y^{\prime }}^{2}+y^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| 12376 | \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.709 |
|
| 12377 |
\begin{align*}
y^{\prime }+2 y&=6 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| 12378 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 12379 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=5 \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{x}-4 \cos \left (x \right )+4 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 12380 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-x_{2}-2 x_{3}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}+3 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 12381 |
\begin{align*}
\left (a^{2} x^{2}+2\right ) y-2 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 12382 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.710 |
|
| 12383 |
\begin{align*}
x^{4} y^{\prime \prime }&=-4 y^{2}+x^{2} y^{\prime } \left (x +y^{\prime }\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.710 |
|
| 12384 |
\begin{align*}
y^{\prime \prime }-9 y&={\mathrm e}^{3 x}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 12385 |
\begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 12386 |
\begin{align*}
x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.710 |
|
| 12387 |
\begin{align*}
x^{2} \left (y-1\right ) y^{\prime \prime }-2 x^{2} {y^{\prime }}^{2}-2 x \left (y-1\right ) y^{\prime }-2 y \left (y-1\right )^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.710 |
|
| 12388 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (a \,x^{3} b +a c \,x^{2}+b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.710 |
|
| 12389 |
\begin{align*}
3 y^{\prime \prime } x -\left (x -2\right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 12390 |
\begin{align*}
\frac {y^{\prime \prime }}{x}+\frac {3 \left (x -4\right ) y^{\prime }}{6+x}+\frac {x^{2} \left (x -2\right ) y}{x -1}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 12391 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| 12392 |
\begin{align*}
x^{\prime }&=x+2 y+z \\
y^{\prime }&=6 x-y \\
z^{\prime }&=-x-2 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 12393 |
\begin{align*}
x^{2} \left (4 x +3\right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (4 x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 12394 |
\begin{align*}
x y^{\prime } \left (y^{\prime }+2\right )&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 12395 | \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) \left (\arctan \left (y^{\prime }\right )+a x \right )+y^{\prime }&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 0.711 |
|
| 12396 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }-3 y^{\prime }+2 y&=x \left (3 x^{3}+1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.711 |
|
| 12397 |
\begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )&=R^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| 12398 |
\begin{align*}
y y^{\prime \prime }&=y^{2} y^{\prime }+{y^{\prime }}^{2} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.711 |
|
| 12399 |
\begin{align*}
y^{\prime \prime }&=\frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (a \left (a +1\right )-a \,x^{2} \left (a +3\right )\right ) y}{x^{2} \left (x^{2}-1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.711 |
|
| 12400 |
\begin{align*}
-y^{\prime }+{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.711 |
|