Question

Find the particular solution to y ′ = 3sin(x) given the general solution is y = C − 3cos(x) and the initial condition y(π) = 1. (5 points)

4 - 3cos(x)
-2 - 3cos(x)
2 - 3cos(x)
-4 - 3cos(x)

Answer 1

`y=C-3\cos`


`y(\pi)=1`

`\implies 1=C-3\cos\pi\implies 1=C+3\implies C=-2`

So the particular solution is


`y=-2-3\cos x`

Answer 2

Hence, the particular solution is:

y= -2-3 cos(x)

Explanation:

We are given a differential equation as:

y ′ = 3sin(x)

It's general solution is given as:

y = C −3cos(x) --------(1)

Now we are given a initial condition as:

y(π) = 1.

We will put the initial condition in the general solution to obtain the value of the constant 'C'.

We will put x=π in the equation (1).

y=C -3 cos(π)

As we know:

cos(π)=-1

Hence,

⇒ 1=C-3×(-1)

⇒ 1=C+3

⇒ C=1-3

⇒ C= -2

Hence, the particular solution is:

y= -2-3 cos(x)