2.1.8 problem 8

Internal problem ID [658]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.2. Integrals as general and particular solutions. Page 16
Problem number : 8
Date solved : Tuesday, September 30, 2025 at 04:05:04 AM
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: 0.021 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 12

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

\begin{align*} y(x)&\to \sin (x) \cos (x)+1 \end{align*}

✓ Sympy. Time used: 0.068 (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)
 

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