Internal problem ID [7411]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 692.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.12 (sec). Leaf size: 19
dsolve(4*x^2*diff(y(x),x$2)+4*x*(1+2*x)*diff(y(x),x)+(4*x-1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{\sqrt {x}}+\frac {c_{2} {\mathrm e}^{-2 x}}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 26
DSolve[4*x^2*y''[x]+4*x*(1+2*x)*y'[x]+(4*x-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 c_1 e^{-2 x}+c_2}{2 \sqrt {x}} \\ \end{align*}