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**bustacap09** Find the value(s) of A such that the solution of the initial-value problem

y'' - 4y = sinx ; y(0)=A, y'(0)=0 is bounded

Answer is A=-1/10

Why is this the solution and how did they come up with it. I am pretty comfortable with laplace transforms and does it have to do with this.

Also

Find the value of A such that the solution of the initial-value problem

y' - 3y = 2e^(-2x) ; y(0)=A

has limit 0 as x goes to infinity.

Answer is A=-2/5

What's the differences in solving these two problems and what kind of solution do i use to solve them?