Internal problem ID [7841]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 356.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime } x^{2}+\frac {\left (x +\frac {3}{4}\right ) y}{4}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve(x^2*diff(y(x),x$2)+1/4*(x+3/4)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \sin \left (\sqrt {x}\right ) x^{\frac {1}{4}}+c_{2} x^{\frac {1}{4}} \cos \left (\sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.068 (sec). Leaf size: 43
DSolve[x^2*y''[x]+1/4*(x+3/4)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-i \sqrt {x}} \sqrt [4]{x} \left (c_1 e^{2 i \sqrt {x}}+i c_2\right ) \]