Question

What initial condition should be imposed to obtain the solution of the initial value problem y" + 3y = 0, y(0) = -3?

1) y(0) = 3
2) y'(0) = -3
3) y(0) = -3
4) y''(0) = -3

Answer 1

The correct initial condition to impose alongside y(0) = -3, for a unique solution to the initial value problem
`y` is
`y'(0) = -3`.

Step-by-step explanation:

The initial value problem given is
`y`, with the initial condition
`y(0) = -3`. To fully determine the solution for this second-order differential equation, we need two initial conditions: one for the function itself,
`y(0)`, and one for its first derivative,
`y'(0)`. The problem statement already gives us
`y(0) = -3`, which satisfies one initial condition. The additional initial condition needed is for
`y'(0)`, the derivative of y with respect to time at t=0, hence the correct answer is
`y(0) = -3`. This value ensures we can find a unique solution for the given differential equation that satisfies both initial conditions.