59.1.778 problem 800

Internal problem ID [9950]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 800
Date solved : Monday, January 27, 2025 at 06:16:05 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

dsolve(x^2*diff(y(x),x$2)+1/4*(x+3/4)*y(x)=0,y(x), singsol=all)
 

\[ y = x^{{1}/{4}} \left (c_{1} \sin \left (\sqrt {x}\right )+c_{2} \cos \left (\sqrt {x}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 43

DSolve[x^2*D[y[x],{x,2}]+1/4*(x+3/4)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-i \sqrt {x}} \sqrt [4]{x} \left (c_1 e^{2 i \sqrt {x}}+i c_2\right ) \]