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 : Wednesday, March 05, 2025 at 05:03:24 AM
CAS classification : [_separable]

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

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

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

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

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

ode=y[x]*D[y[x],x]==Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.391 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)*Derivative(y(x), x) - exp(2*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt {C_{1} + e^{2 x}}, \ y{\left (x \right )} = \sqrt {C_{1} + e^{2 x}}\right ] \]