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 : Saturday, March 29, 2025 at 04:28:17 PM
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*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 9

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

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

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

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

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

✓ Sympy. Time used: 0.204 (sec). Leaf size: 8

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

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