59.1.772 problem 794

Internal problem ID [9944]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 794
Date solved : Monday, January 27, 2025 at 06:16:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 21

dsolve(x^2*diff(y(x),x$2)+6*x*diff(y(x),x)+(4*x^2+6)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} \sin \left (2 x \right )+c_{2} \cos \left (2 x \right )}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 37

DSolve[x^2*D[y[x],{x,2}]+6*x*D[y[x],x]+(4*x^2+6)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {4 c_1 e^{-2 i x}-i c_2 e^{2 i x}}{4 x^3} \]