7.3.27 problem 27

Internal problem ID [67]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 27
Date solved : Tuesday, March 04, 2025 at 10:41:29 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=6 \,{\mathrm e}^{2 x -y} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 13

ode:=diff(y(x),x) = 6*exp(2*x-y(x)); 
ic:=y(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \ln \left (3 \,{\mathrm e}^{2 x}-2\right ) \]

✓ Mathematica. Time used: 0.786 (sec). Leaf size: 15

ode=D[y[x],x]== 6*Exp[2*x-y[x]]; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \log \left (3 e^{2 x}-2\right ) \]

✓ Sympy. Time used: 0.206 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*exp(2*x - y(x)) + Derivative(y(x), x),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \log {\left (3 e^{2 x} - 2 \right )} \]