Question

Find the general solution to 3y" + 27y = 0. Give your answer as ________. In your answer, use ________ and ________ to denote arbitrary constants and the independent variable. Enter as c1 and ________ as c2.

1) c1, c2
2) x, y
3) a, b
4) m, n

Answer 1

The general solution to 3y" + 27y = 0 is y = c1e^(i√3t) + c2e^(-i√3t), where c1 and c2 are arbitrary constants.

Step-by-step explanation:

The given differential equation is 3y" + 27y = 0. To find the general solution, we can assume that the solution takes the form y = e^(rt), where r is a constant. Substituting this into the differential equation, we get the characteristic equation 3r^2 + 27 = 0. Solving this equation, we find that r = ±i√3.

Therefore, the general solution is y = c1e^(i√3t) + c2e^(-i√3t), where c1 and c2 are arbitrary constants.