Question

Find the particular solution to y'=2sin(x) given the general solution is y=C-2cos(x) and the initial condition y(pi/3)=1

Answer 1

ANSWER

The particular solution is:

$y=2-2 \cos(x)$

EXPLANATION

The given Ordinary Differential Equation is

$y'=2 \sin(x)$

The general solution to this Differential equation is:

$y=C-2 \cos(x)$

To find the particular solution, we need to apply the initial conditions (ICs)

$y( \frac{\pi}{3} ) = 1$

This implies that;

$C-2 \cos( \frac{\pi}{3} ) = 1$

$C-2( \frac{1}{2} )= 1$

$C-1= 1$

$C= 1 + 1 = 2$

Hence the particular solution is

$y=2-2 \cos(x)$