59.1.758 problem 780

Internal problem ID [9930]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 780
Date solved : Monday, January 27, 2025 at 06:15:53 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 43

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

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