Internal problem ID [7125]
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]]
\[ \boxed {y^{\prime }-y^{2}=x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 45
dsolve(diff(y(x),x)=x^2+y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-\operatorname {BesselJ}\left (-\frac {3}{4}, \frac {x^{2}}{2}\right ) c_{1} -\operatorname {BesselY}\left (-\frac {3}{4}, \frac {x^{2}}{2}\right )\right ) x}{c_{1} \operatorname {BesselJ}\left (\frac {1}{4}, \frac {x^{2}}{2}\right )+\operatorname {BesselY}\left (\frac {1}{4}, \frac {x^{2}}{2}\right )} \]
✓ Solution by Mathematica
Time used: 0.127 (sec). Leaf size: 169
DSolve[y'[x]==x^2+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2 \left (-2 \operatorname {BesselJ}\left (-\frac {3}{4},\frac {x^2}{2}\right )+c_1 \left (\operatorname {BesselJ}\left (\frac {3}{4},\frac {x^2}{2}\right )-\operatorname {BesselJ}\left (-\frac {5}{4},\frac {x^2}{2}\right )\right )\right )-c_1 \operatorname {BesselJ}\left (-\frac {1}{4},\frac {x^2}{2}\right )}{2 x \left (\operatorname {BesselJ}\left (\frac {1}{4},\frac {x^2}{2}\right )+c_1 \operatorname {BesselJ}\left (-\frac {1}{4},\frac {x^2}{2}\right )\right )} y(x)\to -\frac {x^2 \operatorname {BesselJ}\left (-\frac {5}{4},\frac {x^2}{2}\right )-x^2 \operatorname {BesselJ}\left (\frac {3}{4},\frac {x^2}{2}\right )+\operatorname {BesselJ}\left (-\frac {1}{4},\frac {x^2}{2}\right )}{2 x \operatorname {BesselJ}\left (-\frac {1}{4},\frac {x^2}{2}\right )} \end{align*}