Internal problem ID [7194]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 473.
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 y^{\prime }+\left (4 x^{2}+3\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 19
dsolve(4*x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+(4*x^2+3)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sqrt {x}\, \sin \relax (x )+c_{2} \sqrt {x}\, \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 39
DSolve[4*x^2*y''[x]-4*x*y'[x]+(4*x^2+3)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-i x} \sqrt {x} \left (2 c_1-i c_2 e^{2 i x}\right ) \\ \end{align*}