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*}