74.5.8 problem 8

Internal problem ID [15972]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 08:25:11 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+y&=x \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 19

DSolve[x*D[y[x],x]+y[x]==x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

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