tion. (a) y" + 9my = 0, (b) y(4)-81ny = 0, (a) Verify by differentiation that the function provided solves the differential equa- (b) 7. Separation of variables: Find all solutions to the following differential equations, using separation of variables when necessary. If an initial condition is provided, find the solution to the differential equation satisfying it. dy dx dy dt = x, y(1) = 2 y = sin(3x) = y, y(1) = 2 y = sin(37x) (c) (d) dx dt = xe-y - S tant