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)

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation: