32.9.17 problem Exercise 22, problem 17, page 240

Internal problem ID [5991]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number : Exercise 22, problem 17, page 240
Date solved : Monday, January 27, 2025 at 01:30:26 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 25

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

\[ y \left (x \right ) = \frac {x^{3} \ln \left (x \right )}{2}-\frac {3 x^{3}}{4}+c_{2} x^{2}+c_{1} x \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 32

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

\[ y(x)\to \frac {1}{4} x \left (-3 x^2+2 x^2 \log (x)+4 c_2 x+4 c_1\right ) \]