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)

Hence, the particular solution is:

y= -2-3 cos(x)

Step-by-step 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)

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fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right