Question

Solve the given initial-value problem. D2y dt2 − 4 dy dt − 5y = 0, y(1) = 0, y'(1) = 9

Answer 1

To solve the given initial-value problem, we use the characteristic equation method to find the general solution and then substitute the initial conditions to find the specific solution. The specific solution is y(t) = 9e5t/2 - 9e-t/2.

Step-by-step explanation:

To solve the given initial-value problem D2y/dt2 - 4(dY/dt) - 5y = 0, y(1) = 0, y'(1) = 9, we can use the characteristic equation method. The characteristic equation is r2 - 4r - 5 = 0. Solving this quadratic equation gives us r = 5 or r = -1. Therefore, the general solution is y(t) = C1e5t + C2e-t. Substituting the initial conditions into the general solution, we can find the values of C1 and C2. The specific solution is y(t) = 9e5t/2 - 9e-t/2.