59.1.386 problem 396

Internal problem ID [9558]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 396
Date solved : Monday, January 27, 2025 at 06:04:05 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y&=0 \end{align*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 41

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

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