24.1.6 problem 1(f)

Internal problem ID [4195]
Book : Elementary Differential equations, Chaundy, 1969
Section : Exercises 3, page 60
Problem number : 1(f)
Date solved : Monday, January 27, 2025 at 08:41:47 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+y \ln \left (x \right )&=x^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.083 (sec). Leaf size: 19

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

\[ y(x)\to x^{-x} \left (-1+c_1 e^x\right ) \]