Internal problem ID [7925]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 446.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 y^{\prime \prime } x^{2}+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(4*x^2*diff(y(x),x$2)+(4*x-8*x^2)*diff(y(x),x)+(4*x^2-4*x-1)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{x}}{\sqrt {x}}+c_{2} \sqrt {x}\, {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 21
DSolve[4*x^2*y''[x]+(4*x-8*x^2)*y'[x]+(4*x^2-4*x-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x (c_2 x+c_1)}{\sqrt {x}} \]