7.3.19 problem 19

Internal problem ID [59]
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 : 19
Date solved : Friday, February 07, 2025 at 07:47:20 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \,{\mathrm e} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 9

dsolve([diff(y(x),x)= y(x)*exp(x),y(0) = 2*exp(1)],y(x), singsol=all)
 

\[ y = 2 \,{\mathrm e}^{{\mathrm e}^{x}} \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 12

DSolve[{D[y[x],x]== y[x]*Exp[x],{y[0]==2*Exp[1]}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 e^{e^x} \]