2.3.26 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 : Tuesday, September 30, 2025 at 04:06:32 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*}

✓ Maple. Time used: 0.092 (sec). Leaf size: 13

ode:=diff(y(x),x) = 6*exp(2*x-y(x)); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.566 (sec). Leaf size: 15

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

\begin{align*} y(x)&\to \log \left (3 e^{2 x}-2\right ) \end{align*}

✓ Sympy. Time used: 0.116 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*exp(2*x - y(x)) + Derivative(y(x), x),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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