Im not totally sure how to go about solving second order tri

Im not totally sure how to go about solving second order trigonometric differential equations!

Solve y? = sin(x) if y(0) = 0 and y?(0) = 3. y(x) =

Solution

y\'\' = sin(x)

y\' = -cos(x) + c

y\'(0) = 3

Therefore, -1+c = 3 => c = 4

y\'(x) = 4-cos(x)

y = 4x-sin(x)+k

y(0) = 0

Therefore, 4.0-sin(0) + k = 0 => k=0

Therefore, y = 4x-sin(x)