Internal problem ID [7423]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 704.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (-\frac {1}{4} x -x^{2}\right ) y^{\prime }-\frac {5 y x}{16}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve(x^2*(1-4*x)*diff(y(x),x$2)+((1-(5/4))*x-(6-4*(5/4))*x^2)*diff(y(x),x)+(5/4)*(1-(5/4))*x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \hypergeom \left (\left [-\frac {5}{8}, -\frac {1}{8}\right ], \left [-\frac {1}{4}\right ], 4 x \right )+c_{2} x^{\frac {5}{4}} \hypergeom \left (\left [\frac {5}{8}, \frac {9}{8}\right ], \left [\frac {9}{4}\right ], 4 x \right ) \]
✓ Solution by Mathematica
Time used: 0.237 (sec). Leaf size: 111
DSolve[x^2*(1-4*x)*y''[x]+((1-(5/4))*x-(6-4*(5/4))*x^2)*y'[x]+(5/4)*(1-(5/4))*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [8]{x} \sqrt [4]{4 x-1} \left (5 c_1 \left (\sqrt {4 x-1}-i\right )^{5/4}+i c_2 \left (\sqrt {4 x-1}+i\right )^{5/4}\right )}{5 \sqrt [4]{1-4 x} \sqrt [8]{\sqrt {4 x-1}-i} \sqrt [8]{\sqrt {4 x-1}+i}} \\ \end{align*}