..ooo Verizon 10:24 PM webwork3.uncc.edu Previous Problem List Next (1 point) (a

Question

..ooo Verizon 10:24 PM webwork3.uncc.edu Previous Problem List Next (1 point) (a) Find the general solution of the differential equation y"(t) + 36y(t) = 0. general solution- (Use the letters A and B for any constants you have in your solution.,) (b) For each of the following initial conditions, find a particular solution. (i y(0) = 0, y' (0) = 1: y = (ii) y(0) = 1, y' (0) = 0: y = (iii) y(0) = 1, y(1) = 0: y = (iv) y(0) = 0, y(1) = 1: y = (On a sheet of paper, sketch a graph of the solutions you found in part (b) to see how they differ.) Note: You can earn partial credit on this problem.

Explanation / Answer

ANSWER:

y??(t)+36y(t)=0

auxiliary eq. is

m^2 + 36 = 0

or

m^2 + 6^2 = 0

or

m^2 = -6^2

or

m = 6i, -6i

so, the general solution is

y(t) = ACos(6t) + Bsin(6t)

(i) y(0)=0, y?(0)=1

0 = A

y'(t) = -6ASin(6t) + 6BCos(6t)

put y' = 1, t = 0

1 = 6B

or

B = 1/6

so, the particular solution is

y(t) = [sin(6t)]/6

(ii) y(0)=1, y?(0)=0

1 = A

y'(t) = -6ASin(6t) + 6BCos(6t)

put y' = 0, t = 0

0 = 6B

or

B =0

the particular solution is

y(t) = Cos(6t)

similarly solve the remaining

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