8.3.26 problem 27

Internal problem ID [702]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 27
Date solved : Monday, January 27, 2025 at 02:58:29 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*}

Solution by Maple

Time used: 0.019 (sec). Leaf size: 13

dsolve([diff(y(x),x) = 6*exp(2*x-y(x)),y(0) = 0],y(x), singsol=all)
 
\[ y = \ln \left (-2+3 \,{\mathrm e}^{2 x}\right ) \]

Solution by Mathematica

Time used: 0.742 (sec). Leaf size: 15

DSolve[{D[y[x],x] == 6*Exp[2*x-y[x]],y[0]==0},y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to \log \left (3 e^{2 x}-2\right ) \]