50.1.25 problem 3(a)

Internal problem ID [7797]
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)
Date solved : Monday, January 27, 2025 at 03:23:22 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (1\right )&=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)
 

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

✓ Solution by Mathematica

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

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

\[ y(x)\to e^x (x-1)+3 \]