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**1. Homework Statement**

Find a second-order initial-value problem whose solution is sin at

**3. The Attempt at a Solution**

so i know that

y' = a cos at

y" = -a^2 sin at

but the solution says that

"Then y(t) = sin at is

a solution to 2 y ''+ a y = 0 . Our initial conditions must be y(0) = 0, y '(0) = a ."

how do i know that it's 2y'' + a y? how come it couldn't be something else like y''+y'+ y?

thanks