59.1.239 problem 242

Internal problem ID [9411]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 242
Date solved : Monday, January 27, 2025 at 06:02:31 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 24

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

\[ y = \frac {2 c_{2} {\mathrm e}^{-2 x} x +c_{2} {\mathrm e}^{-2 x}+c_{1}}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.227 (sec). Leaf size: 33

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

\[ y(x)\to \frac {c_2 \int _1^xe^{-2 K[1]} K[1]dK[1]+c_1}{\sqrt {x}} \]