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

-2cos(x)

3-2cos(x)

2-3cos(x)

-1-2cos(x)

Answer 1

The particular solution is:

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

Step-by-step 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( (\pi)/(3) ) = 1`

This implies that;

`C-2 \cos( (\pi)/(3) ) = 1`

`C-2( (1)/(2) )= 1`

`C-1= 1`

`C= 1 + 1 = 2`

Hence the particular solution is

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