59.1.43 problem 45

Internal problem ID [9215]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 45
Date solved : Monday, January 27, 2025 at 05:52:09 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 +3\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 14

dsolve(4*x^2*diff(y(x),x$2)-4*x*(x+1)*diff(y(x),x)+(2*x+3)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 25

DSolve[4*x^2*D[y[x],{x,2}]-4*x*(x+1)*D[y[x],x]+(2*x+3)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {e} \sqrt {x} \left (c_2 e^x+c_1\right ) \]