9.20 problem Exercise 22, problem 20, page 240

Internal problem ID [4142]

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.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y-\frac {1}{x}=0} \end {gather*}

Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

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

\[ y \relax (x ) = \frac {c_{1}}{x}+\sqrt {x}\, c_{2}-\frac {3 \ln \relax (x )+2}{9 x} \]

Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 31

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

\begin{align*} y(x)\to \frac {9 c_2 x^{3/2}-3 \log (x)-2+9 c_1}{9 x} \\ \end{align*}