32.9.20 problem Exercise 22, problem 20, page 240

Internal problem ID [5994]
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 20, page 240
Date solved : Monday, January 27, 2025 at 01:30:33 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y&=\frac {1}{x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 31

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

\[ y(x)\to \frac {9 c_2 x^{3/2}-3 \log (x)-2+9 c_1}{9 x} \]