59.1.514 problem 530

Internal problem ID [9686]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 530
Date solved : Monday, January 27, 2025 at 06:13:05 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y \left (1+x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 29

dsolve(2*x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+(1+x)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 60

DSolve[2*x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+(1+x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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