50.1.3 problem 1(c)

Internal problem ID [7775]
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 : 1(c)
Date solved : Monday, January 27, 2025 at 03:21:43 PM
CAS classification : [_separable]

\begin{align*} y^{\prime } y&={\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 25

dsolve(y(x)*diff(y(x),x)=exp(2*x),y(x), singsol=all)
 

\begin{align*} y &= \sqrt {{\mathrm e}^{2 x}+c_{1}} \\ y &= -\sqrt {{\mathrm e}^{2 x}+c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.584 (sec). Leaf size: 39

DSolve[y[x]*D[y[x],x]==Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {e^{2 x}+2 c_1} \\ y(x)\to \sqrt {e^{2 x}+2 c_1} \\ \end{align*}