70.1.32 problem 32

Internal problem ID [18618]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 32
Date solved : Thursday, October 02, 2025 at 03:17:12 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {6-{\mathrm e}^{x}}{3+2 y} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.226 (sec). Leaf size: 19

ode:=diff(y(x),x) = (6-exp(x))/(3+2*y(x)); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {3}{2}+\frac {\sqrt {13-4 \,{\mathrm e}^{x}+24 x}}{2} \]

✓ Mathematica. Time used: 0.51 (sec). Leaf size: 25

ode=D[y[x],x]==(6-Exp[x])/(3+2*y[x]); 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} \left (\sqrt {24 x-4 e^x+13}-3\right ) \end{align*}

✓ Sympy. Time used: 0.364 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + (exp(x) - 6)/(2*y(x) + 3),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\sqrt {24 x - 4 e^{x} + 13}}{2} - \frac {3}{2} \]