59.1.363 problem 370

Internal problem ID [9535]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 370
Date solved : Monday, January 27, 2025 at 06:03:50 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 29

dsolve(diff(y(x),x$2)+1/(2*x^4)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.096 (sec). Leaf size: 50

DSolve[D[y[x],{x,2}]+1/(2*x^4)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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