10.2.24 problem 24

Internal problem ID [1152]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 24
Date solved : Tuesday, March 04, 2025 at 12:12:35 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.157 (sec). Leaf size: 19

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

\[ y = -\frac {3}{2}+\frac {\sqrt {13-4 \,{\mathrm e}^{x}+8 x}}{2} \]

✓ Mathematica. Time used: 0.632 (sec). Leaf size: 25

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

\[ y(x)\to \frac {1}{2} \left (\sqrt {8 x-4 e^x+13}-3\right ) \]

✓ Sympy. Time used: 0.571 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \frac {\sqrt {8 x - 4 e^{x} + 13}}{2} - \frac {3}{2} \]