Internal problem ID [6383]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 90.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-y^{2}-x -x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 280
dsolve(diff(y(x),x)-y(x)^2-x-x^2=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {\left (48 i c_{1} x^{2}+4 c_{1} x^{2}+48 i c_{1} x +4 c_{1} x +12 i c_{1}+c_{1}\right ) \hypergeom \left (\left [\frac {7}{4}-\frac {i}{16}\right ], \left [\frac {5}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )}{24 \left (\left (2 c_{1} x +c_{1}\right ) \hypergeom \left (\left [\frac {3}{4}-\frac {i}{16}\right ], \left [\frac {3}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )+\hypergeom \left (\left [\frac {1}{4}-\frac {i}{16}\right ], \left [\frac {1}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )\right )}-\frac {\left (24 i x +6 x +12 i+3\right ) \hypergeom \left (\left [\frac {5}{4}-\frac {i}{16}\right ], \left [\frac {3}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )}{24 \left (\left (2 c_{1} x +c_{1}\right ) \hypergeom \left (\left [\frac {3}{4}-\frac {i}{16}\right ], \left [\frac {3}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )+\hypergeom \left (\left [\frac {1}{4}-\frac {i}{16}\right ], \left [\frac {1}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )\right )}-\frac {\left (-48 i c_{1} x^{2}-48 i c_{1} x -12 i c_{1}+48 c_{1}\right ) \hypergeom \left (\left [\frac {3}{4}-\frac {i}{16}\right ], \left [\frac {3}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )+\left (-24 i x -12 i\right ) \hypergeom \left (\left [\frac {1}{4}-\frac {i}{16}\right ], \left [\frac {1}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )}{24 \left (\left (2 c_{1} x +c_{1}\right ) \hypergeom \left (\left [\frac {3}{4}-\frac {i}{16}\right ], \left [\frac {3}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )+\hypergeom \left (\left [\frac {1}{4}-\frac {i}{16}\right ], \left [\frac {1}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.319 (sec). Leaf size: 233
DSolve[y'[x]-y[x]^2-x-x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {i \left ((2 x+1) D_{-\frac {1}{2}-\frac {i}{8}}\left (\left (-\frac {1}{2}+\frac {i}{2}\right ) (2 x+1)\right )+(2+2 i) D_{\frac {1}{2}-\frac {i}{8}}\left (\left (-\frac {1}{2}+\frac {i}{2}\right ) (2 x+1)\right )-c_1 (2 x+1) D_{-\frac {1}{2}+\frac {i}{8}}\left ((1+i) x+\left (\frac {1}{2}+\frac {i}{2}\right )\right )+(2-2 i) c_1 D_{\frac {1}{2}+\frac {i}{8}}\left ((1+i) x+\left (\frac {1}{2}+\frac {i}{2}\right )\right )\right )}{2 \left (D_{-\frac {1}{2}-\frac {i}{8}}\left (\left (-\frac {1}{2}+\frac {i}{2}\right ) (2 x+1)\right )+c_1 D_{-\frac {1}{2}+\frac {i}{8}}\left ((1+i) x+\left (\frac {1}{2}+\frac {i}{2}\right )\right )\right )} \\ y(x)\to \frac {(1+i) D_{\frac {1}{2}+\frac {i}{8}}\left ((1+i) x+\left (\frac {1}{2}+\frac {i}{2}\right )\right )}{D_{-\frac {1}{2}+\frac {i}{8}}\left ((1+i) x+\left (\frac {1}{2}+\frac {i}{2}\right )\right )}-\frac {1}{2} i (2 x+1) \\ \end{align*}