59.1.331 problem 338

Internal problem ID [9503]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 338
Date solved : Monday, January 27, 2025 at 06:03:32 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 25

dsolve(16*x^2*diff(y(x),x$2)+32*x*diff(y(x),x)+(x^4-12)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} \sin \left (\frac {x^{2}}{8}\right )+c_{2} \cos \left (\frac {x^{2}}{8}\right )}{x^{{3}/{2}}} \]

✓ Solution by Mathematica

Time used: 0.112 (sec). Leaf size: 48

DSolve[16*x^2*D[y[x],{x,2}]+32*x*D[y[x],x]+(x^4-12)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-\frac {1}{2}-\frac {i x^2}{8}} \left (c_1-2 i c_2 e^{1+\frac {i x^2}{4}}\right )}{x^{3/2}} \]