Internal problem ID [6996]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 265.
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 }-\frac {x y^{\prime }}{2}-\frac {3 y x}{4}=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-(3/2))*x-(6-4*(3/2))*x^2)*diff(y(x),x)+(3/2)*(1-(3/2))*x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \hypergeom \left (\left [-\frac {3}{4}, -\frac {1}{4}\right ], \left [-\frac {1}{2}\right ], 4 x \right )+c_{2} x^{\frac {3}{2}} \hypergeom \left (\left [\frac {3}{4}, \frac {5}{4}\right ], \left [\frac {5}{2}\right ], 4 x \right ) \]
✓ Solution by Mathematica
Time used: 0.279 (sec). Leaf size: 111
DSolve[x^2*(1-4*x)*y''[x]+((1-(3/2))*x-(6-4*(3/2))*x^2)*y'[x]+(3/2)*(1-(3/2))*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [4]{x} \sqrt [4]{4 x-1} \left (6 c_1 \left (\sqrt {4 x-1}-i\right )^{3/2}+i c_2 \left (\sqrt {4 x-1}+i\right )^{3/2}\right )}{6 \sqrt [4]{1-4 x} \sqrt [4]{\sqrt {4 x-1}-i} \sqrt [4]{\sqrt {4 x-1}+i}} \\ \end{align*}