Internal problem ID [10787]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 35.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-x^{2}+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 44
dsolve(diff(y(x),x)=x^2-y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x \left (\operatorname {BesselI}\left (-\frac {3}{4}, \frac {x^{2}}{2}\right ) c_{1} -\operatorname {BesselK}\left (\frac {3}{4}, \frac {x^{2}}{2}\right )\right )}{\operatorname {BesselI}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) c_{1} +\operatorname {BesselK}\left (\frac {1}{4}, \frac {x^{2}}{2}\right )} \]
✓ Solution by Mathematica
Time used: 0.123 (sec). Leaf size: 103
DSolve[y'[x]==x^2-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {i x \left (\operatorname {BesselJ}\left (-\frac {3}{4},\frac {i x^2}{2}\right )-c_1 \operatorname {BesselJ}\left (\frac {3}{4},\frac {i x^2}{2}\right )\right )}{\operatorname {BesselJ}\left (\frac {1}{4},\frac {i x^2}{2}\right )+c_1 \operatorname {BesselJ}\left (-\frac {1}{4},\frac {i x^2}{2}\right )} \\ y(x)\to \frac {x \operatorname {BesselI}\left (\frac {3}{4},\frac {x^2}{2}\right )}{\operatorname {BesselI}\left (-\frac {1}{4},\frac {x^2}{2}\right )} \\ \end{align*}