Internal problem ID [6329]
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]
Solve \begin {gather*} \boxed {u^{\prime }+u^{2}-\frac {1}{x^{\frac {4}{5}}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 46
dsolve(diff(u(x),x)+u(x)^2=x^(-4/5),u(x), singsol=all)
\[ u \relax (x ) = -\frac {-\BesselI \left (-\frac {1}{6}, \frac {5 x^{\frac {3}{5}}}{3}\right ) c_{1}+\BesselK \left (\frac {1}{6}, \frac {5 x^{\frac {3}{5}}}{3}\right )}{x^{\frac {2}{5}} \left (c_{1} \BesselI \left (\frac {5}{6}, \frac {5 x^{\frac {3}{5}}}{3}\right )+\BesselK \left (\frac {5}{6}, \frac {5 x^{\frac {3}{5}}}{3}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.175 (sec). Leaf size: 123
DSolve[u'[x]+u[x]^2==x^(-4/5),u[x],x,IncludeSingularSolutions -> True]
\begin{align*} u(x)\to \frac {i \left (J_{-\frac {1}{6}}\left (\frac {5}{3} i x^{3/5}\right )-c_1 J_{\frac {1}{6}}\left (\frac {5}{3} i x^{3/5}\right )\right )}{x^{2/5} \left (J_{\frac {5}{6}}\left (\frac {5}{3} i x^{3/5}\right )+c_1 J_{-\frac {5}{6}}\left (\frac {5}{3} i x^{3/5}\right )\right )} \\ u(x)\to \frac {I_{\frac {1}{6}}\left (\frac {5 x^{3/5}}{3}\right )}{x^{2/5} I_{-\frac {5}{6}}\left (\frac {5 x^{3/5}}{3}\right )} \\ \end{align*}