Final answer:
To find a positive value of K that satisfies the differential equation, substitute Y = cos(Kt) into the equation and solve for K. The positive value of K that satisfies the equation is K = 2.
Step-by-step explanation:
The given differential equation is D²y/Dt² + 4y = 0. We are given the function Y = cos(Kt). To find a positive value of K that satisfies the differential equation, we need to substitute Y into the equation and solve for K.
Substituting Y = cos(Kt) into the differential equation, we have (-K²)(cos(Kt)) + 4(cos(Kt)) = 0. Simplifying, we get -K² + 4 = 0. Rearranging the equation, we have K² = 4. Taking the square root of both sides, we get K = ±2.
Since we are looking for a positive value of K, the answer is K = 2.