59.1.341 problem 348

Internal problem ID [9513]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 348
Date solved : Monday, January 27, 2025 at 06:03:38 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+2 y^{\prime }+4 y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 37

DSolve[x*D[y[x],{x,2}]+2*D[y[x],x]+4*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {4 c_1 e^{-2 i x}-i c_2 e^{2 i x}}{4 x} \]