59.1.377 problem 384

Internal problem ID [9549]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 384
Date solved : Monday, January 27, 2025 at 06:03:59 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

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

\[ y = \frac {c_{1} {\mathrm e}^{-3 x}+c_{2} \left (9 x^{2}-6 x +2\right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.856 (sec). Leaf size: 52

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

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