PROBLEM 4E

Verify that y = sin 3t + 2 cos 3t is a solution to the initial value problem

Find the maximum of

solution : Step 1: In this problem, we have to verify that y = sin3t + 2cos3t is a solution to the initial value problem 2y + 18 y = 0; y(0) = 2, y(0) = 3.and we have to find the maximum of |(t) |or < t < . Step 2: We given, that y = sin3t + 2cos3t is a solution to the initial value problem 2y + 18 y = 0. We know that “every solution is satisfying own equation”. So, if y = sin3t + 2cos3t is a solution of the equation 2y + 18 y = 0, then the solution y = sin3t + 2cos3t must be satisfy the equation 2y + 18 y = 0.