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*}