59.1.657 problem 674

Internal problem ID [9829]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 674
Date solved : Monday, January 27, 2025 at 06:14:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 17

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

\[ y = \left (\operatorname {Ei}_{1}\left (-x \right ) c_{2} +c_{1} \right ) \sqrt {x} \]

✓ Solution by Mathematica

Time used: 0.206 (sec). Leaf size: 33

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

\[ y(x)\to \sqrt {x} \left (c_2 \int _1^x\frac {e^{K[1]}}{K[1]}dK[1]+c_1\right ) \]