4.2.25 problem 25

Internal problem ID [1153]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 25
Date solved : Tuesday, September 30, 2025 at 04:24:42 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {2 \cos \left (2 x \right )}{3+2 y} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.330 (sec). Leaf size: 18

ode:=diff(y(x),x) = 2*cos(2*x)/(3+2*y(x)); 
ic:=[y(0) = -1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {3}{2}+\frac {\sqrt {1+4 \sin \left (2 x \right )}}{2} \]

✓ Mathematica. Time used: 0.098 (sec). Leaf size: 23

ode=D[y[x],x] == 2*Cos[2*x]/(3+2*y[x]); 
ic=y[0]==-1; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.367 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 2*cos(2*x)/(2*y(x) + 3),0) 
ics = {y(0): -1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\sqrt {4 \sin {\left (2 x \right )} + 1}}{2} - \frac {3}{2} \]