1.6 problem 1(f)

Internal problem ID [2525]

Book: Elementary Differential equations, Chaundy, 1969
Section: Exercises 3, page 60
Problem number: 1(f).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

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

Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

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

\[ y \relax (x ) = -x^{-x}+x^{-x} {\mathrm e}^{x} c_{1} \]

Solution by Mathematica

Time used: 0.086 (sec). Leaf size: 19

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

\begin{align*} y(x)\to x^{-x} \left (-1+c_1 e^x\right ) \\ \end{align*}