Internal problem ID [5353]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y y^{\prime }-{\mathrm e}^{2 x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(y(x)*diff(y(x),x)=exp(2*x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {{\mathrm e}^{2 x}+c_{1}} \\ y \left (x \right ) = -\sqrt {{\mathrm e}^{2 x}+c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.58 (sec). Leaf size: 39
DSolve[y[x]*y'[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*}