47.5.3 problem 3

Internal problem ID [7492]
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 : 3
Date solved : Monday, January 27, 2025 at 03:02:13 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 22

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

\[ y = \frac {c_{1}}{x}+c_{2} x +\frac {\left (x +3 \ln \left (x \right )\right ) x}{3} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 31

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

\[ y(x)\to \frac {x^2}{3}+x \log (x)+\left (-\frac {1}{2}+c_2\right ) x+\frac {c_1}{x} \]