2.3.18 problem 19

Internal problem ID [694]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 19
Date solved : Tuesday, September 30, 2025 at 04:06:17 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.018 (sec). Leaf size: 9

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 12

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

\begin{align*} y(x)&\to 2 e^{e^x} \end{align*}

✓ Sympy. Time used: 0.153 (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)
 

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