47.5.2 problem 2

Internal problem ID [7491]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 2. Linear homogeneous equations. Section 2.3.4 problems. page 104
Problem number : 2
Date solved : Monday, January 27, 2025 at 03:02:11 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+x y^{\prime }-y&=x^{2}+2 x \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.323 (sec). Leaf size: 31

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

\[ y(x)\to -c_2 x \operatorname {ExpIntegralEi}(-x)+x^2+c_1 x-c_2 e^{-x} \]