Find the particular solution to y ' = 2sin(x) given the general solution is y = C - 2cos(x) and the initial condition y of pi over 3 equals 1 . (5 points) -2cos(x)
closeIncorrect
3 - 2cos(x)
checkCorrect
2 - 2cos(x)
-1 - 2cos(x)

Step-by-step explanation:

We have the differential:

With the general solution:

And we want to find the particular solution such that it satisfies the initial condition:

So, we have:

Substituting π/3 for x and 1 for y yields:

Solve for C. Evaluate:

Simplify:

Hence:

Therefore, our particular solution will be:

Hence, our answer is C

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1