15.8 problem 416

Internal problem ID [3162]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 15
Problem number: 416.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime } x \ln \relax (x )-a x \left (\ln \relax (x )+1\right )+y=0} \end {gather*}

Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

dsolve(diff(y(x),x)*x*ln(x) = a*x*(1+ln(x))-y(x),y(x), singsol=all)
 

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

Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 16

DSolve[y'[x] x Log[x]==a x(1+Log[x])-y[x],y[x],x,IncludeSingularSolutions -> True]
 

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