Internal problem ID [6328]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 39.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
\[ \boxed {u^{\prime }+u^{2}-\frac {1}{x^{\frac {4}{5}}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 46
dsolve(diff(u(x),x)+u(x)^2=x^(-4/5),u(x), singsol=all)
\[ u \left (x \right ) = \frac {\operatorname {BesselI}\left (-\frac {1}{6}, \frac {5 x^{\frac {3}{5}}}{3}\right ) c_{1} -\operatorname {BesselK}\left (\frac {1}{6}, \frac {5 x^{\frac {3}{5}}}{3}\right )}{x^{\frac {2}{5}} \left (c_{1} \operatorname {BesselI}\left (\frac {5}{6}, \frac {5 x^{\frac {3}{5}}}{3}\right )+\operatorname {BesselK}\left (\frac {5}{6}, \frac {5 x^{\frac {3}{5}}}{3}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.233 (sec). Leaf size: 139
DSolve[u'[x]+u[x]^2==x^(-4/5),u[x],x,IncludeSingularSolutions -> True]
\begin{align*} u(x)\to \frac {(-1)^{5/6} \operatorname {Gamma}\left (\frac {11}{6}\right ) \operatorname {BesselI}\left (-\frac {1}{6},\frac {5 x^{3/5}}{3}\right )+c_1 \operatorname {Gamma}\left (\frac {1}{6}\right ) \operatorname {BesselI}\left (\frac {1}{6},\frac {5 x^{3/5}}{3}\right )}{x^{2/5} \left ((-1)^{5/6} \operatorname {Gamma}\left (\frac {11}{6}\right ) \operatorname {BesselI}\left (\frac {5}{6},\frac {5 x^{3/5}}{3}\right )+c_1 \operatorname {Gamma}\left (\frac {1}{6}\right ) \operatorname {BesselI}\left (-\frac {5}{6},\frac {5 x^{3/5}}{3}\right )\right )} \\ u(x)\to \frac {\operatorname {BesselI}\left (\frac {1}{6},\frac {5 x^{3/5}}{3}\right )}{x^{2/5} \operatorname {BesselI}\left (-\frac {5}{6},\frac {5 x^{3/5}}{3}\right )} \\ \end{align*}