78.1.39 problem 4 (a)

Internal problem ID [18015]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 4 (a)
Date solved : Thursday, March 13, 2025 at 11:19:16 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&={\mathrm e}^{3 x -2 y} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.077 (sec). Leaf size: 20

ode:=diff(y(x),x) = exp(3*x-2*y(x)); 
ic:=y(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {\ln \left (3\right )}{2}+\frac {\ln \left (1+2 \,{\mathrm e}^{3 x}\right )}{2} \]

✓ Mathematica. Time used: 0.828 (sec). Leaf size: 23

ode=D[y[x],x]==Exp[3*x-2*y[x]]; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} \log \left (\frac {1}{3} \left (2 e^{3 x}+1\right )\right ) \]

✓ Sympy. Time used: 0.435 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-exp(3*x - 2*y(x)) + Derivative(y(x), x),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\log {\left (6 e^{3 x} + 3 \right )}}{2} - \log {\left (3 \right )} \]