59.1.327 problem 334

Internal problem ID [9499]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 334
Date solved : Monday, January 27, 2025 at 06:03:29 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 21

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(36*x^2-1/4)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} \sin \left (6 x \right )+c_{2} \cos \left (6 x \right )}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 39

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]+(36*x^2-1/4)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-6 i x} \left (12 c_1-i c_2 e^{12 i x}\right )}{12 \sqrt {x}} \]