3.8 problem 8

Internal problem ID [4260]

Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section: Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page 403
Problem number: 8.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {x \ln \relax (x ) y^{\prime }+y-\ln \relax (x )=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 15

dsolve((x*ln(x))*diff(y(x),x)+y(x)=ln(x),y(x), singsol=all)
 

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

Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 19

DSolve[(x*Log[x])*y'[x]+y[x]==Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {\log (x)}{2}+\frac {c_1}{\log (x)} \\ \end{align*}