59.1.326 problem 333

Internal problem ID [9498]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 333
Date solved : Monday, January 27, 2025 at 06:03:29 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 43

dsolve(4*x^2*diff(y(x),x$2)+4*x*diff(y(x),x)+(4*x^2-25)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {-3 c_{2} \left (i x -\frac {1}{3} x^{2}+1\right ) {\mathrm e}^{-i x}+3 \left (i x +\frac {1}{3} x^{2}-1\right ) c_{1} {\mathrm e}^{i x}}{x^{{5}/{2}}} \]

✓ Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 59

DSolve[4*x^2*D[y[x],{x,2}]+4*x*D[y[x],x]+(4*x^2-25)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {\sqrt {\frac {2}{\pi }} \left (\left (-c_2 x^2+3 c_1 x+3 c_2\right ) \cos (x)+\left (c_1 \left (x^2-3\right )+3 c_2 x\right ) \sin (x)\right )}{x^{5/2}} \]