67.3.16 problem 4.4 (f)

Internal problem ID [16337]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.4 (f)
Date solved : Thursday, October 02, 2025 at 01:21:00 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 24

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

\[ y = \frac {\ln \left (3\right )}{3}-\frac {\ln \left (2\right )}{3}+\frac {\ln \left ({\mathrm e}^{2 x}+2 c_1 \right )}{3} \]

✓ Mathematica. Time used: 0.63 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to \frac {1}{3} \log \left (\frac {3}{2} \left (e^{2 x}+2 c_1\right )\right ) \end{align*}

✓ Sympy. Time used: 0.943 (sec). Leaf size: 71

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

\[ \left [ y{\left (x \right )} = \frac {\log {\left (C_{1} + \frac {3 e^{2 x}}{2} \right )}}{3}, \ y{\left (x \right )} = \log {\left (\frac {\left (-1 - \sqrt {3} i\right ) \sqrt [3]{C_{1} + \frac {3 e^{2 x}}{2}}}{2} \right )}, \ y{\left (x \right )} = \log {\left (\frac {\left (-1 + \sqrt {3} i\right ) \sqrt [3]{C_{1} + \frac {3 e^{2 x}}{2}}}{2} \right )}\right ] \]