7.1.8 problem 8

Internal problem ID [8]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.2. Problems at page 17
Problem number : 8
Date solved : Saturday, March 29, 2025 at 04:25:33 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.023 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 12

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

\[ y(x)\to \sin (x) \cos (x)+1 \]

✓ Sympy. Time used: 0.130 (sec). Leaf size: 10

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

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