1.25 problem 3(a)

Internal problem ID [5376]

Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number: 3(a).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_quadrature]

Solve \begin {gather*} \boxed {y^{\prime }-x \,{\mathrm e}^{x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 3] \end {align*}

Solution by Maple

Time used: 0.009 (sec). Leaf size: 12

dsolve([diff(y(x),x)=x*exp(x),y(1) = 3],y(x), singsol=all)
 

\[ y \relax (x ) = \left (x -1\right ) {\mathrm e}^{x}+3 \]

Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 14

DSolve[{y'[x]==x*Exp[x],{y[1]==3}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^x (x-1)+3 \\ \end{align*}