Internal problem ID [6372]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 80.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Riccati, _special]]
Solve \begin {gather*} \boxed {y^{\prime }-x^{2}-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 45
dsolve(diff(y(x),x)=x^2+y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (-\BesselJ \left (-\frac {3}{4}, \frac {x^{2}}{2}\right ) c_{1}-\BesselY \left (-\frac {3}{4}, \frac {x^{2}}{2}\right )\right ) x}{c_{1} \BesselJ \left (\frac {1}{4}, \frac {x^{2}}{2}\right )+\BesselY \left (\frac {1}{4}, \frac {x^{2}}{2}\right )} \]
✓ Solution by Mathematica
Time used: 0.112 (sec). Leaf size: 93
DSolve[y'[x]==x^2+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x \left (-J_{-\frac {3}{4}}\left (\frac {x^2}{2}\right )+c_1 J_{\frac {3}{4}}\left (\frac {x^2}{2}\right )\right )}{J_{\frac {1}{4}}\left (\frac {x^2}{2}\right )+c_1 J_{-\frac {1}{4}}\left (\frac {x^2}{2}\right )} \\ y(x)\to \frac {x J_{\frac {3}{4}}\left (\frac {x^2}{2}\right )}{J_{-\frac {1}{4}}\left (\frac {x^2}{2}\right )} \\ \end{align*}