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 : Friday, February 07, 2025 at 07:47:38 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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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