78.1.3 problem 1 (c)

Internal problem ID [17987]
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 : Monday, March 31, 2025 at 04:53:14 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.005 (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: 0.586 (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: 0.360 (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)
 

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