44.5.7 problem 7

Internal problem ID [7069]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 7
Date solved : Wednesday, March 05, 2025 at 04:05:08 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 26

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

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

✓ Mathematica. Time used: 0.861 (sec). Leaf size: 24

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

\[ y(x)\to -\frac {1}{2} \log \left (-\frac {2}{3} \left (e^{3 x}+3 c_1\right )\right ) \]

✓ Sympy. Time used: 0.537 (sec). Leaf size: 51

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

\[ \left [ y{\left (x \right )} = \frac {\log {\left (- \frac {1}{C_{1} + e^{3 x}} \right )}}{2} - \log {\left (2 \right )} + \frac {\log {\left (6 \right )}}{2}, \ y{\left (x \right )} = \log {\left (- \sqrt {- \frac {1}{C_{1} + e^{3 x}}} \right )} - \log {\left (2 \right )} + \frac {\log {\left (6 \right )}}{2}\right ] \]