Internal problem ID [14237]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime } x +y=x \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(x*diff(y(x),x)+y(x)=x*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-1+x \right ) {\mathrm e}^{x}+c_{1}}{x} \]
✓ Solution by Mathematica
Time used: 0.078 (sec). Leaf size: 19
DSolve[x*y'[x]+y[x]==x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x (x-1)+c_1}{x} \]