59.1.266 problem 269

Internal problem ID [9438]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 269
Date solved : Monday, January 27, 2025 at 06:02:49 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.100 (sec). Leaf size: 35

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

\[ y = \frac {c_{2} {\mathrm e}^{-\frac {1}{x}} \operatorname {hypergeom}\left (\left [2\right ], \left [-\frac {1}{2}\right ], \frac {1}{x}\right ) x^{{5}/{2}}+5 c_{1} x +2 c_{1}}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.509 (sec). Leaf size: 65

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

\[ y(x)\to \frac {\sqrt {e} (5 x+2) \left (c_2 \int _1^x\frac {25 e^{-\frac {5}{2}-\frac {1}{K[1]}} K[1]^{5/2}}{(5 K[1]+2)^2}dK[1]+c_1\right )}{5 \sqrt {x}} \]