78.1.3 problem 1 (c)

Internal problem ID [18058]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 1 (c)
Date solved : Tuesday, January 28, 2025 at 11:23:35 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.034 (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: 0.586 (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*}