59.1.247 problem 250

Internal problem ID [9419]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 250
Date solved : Monday, January 27, 2025 at 06:02:37 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 23

dsolve(4*x^2*diff(y(x),x$2)+4*x*(1-x)*diff(y(x),x)+(2*x-9)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{x} c_{1} +c_{2} \left (x^{2}+2 x +2\right )}{x^{{3}/{2}}} \]

✓ Solution by Mathematica

Time used: 0.236 (sec). Leaf size: 38

DSolve[4*x^2*D[y[x],{x,2}]+4*x*(1-x)*D[y[x],x]+(2*x-9)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x \left (c_2 \int _1^xe^{-K[1]} K[1]^2dK[1]+c_1\right )}{x^{3/2}} \]