Internal problem ID [7428]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 709.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Jacobi]
Solve \begin {gather*} \boxed {x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 26
dsolve(x*(1-x)*diff(y(x),x$2)+(3/2-2*x)*diff(y(x),x)-1/4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{\sqrt {x}}+\frac {c_{2} \ln \left (-\frac {1}{2}+x +\sqrt {\left (x -1\right ) x}\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 50
DSolve[x*(1-x)*y''[x]+(3/2-2*x)*y'[x]-1/4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\frac {2 c_2 \sqrt {1-x} \log \left (\sqrt {x-1}-\sqrt {x}\right )}{\sqrt {x-1}}+c_1}{\sqrt {x}} \\ \end{align*}