Differential Equations.

Question

Given that y(t)=c1e+4t+c2e^-4t is a solution to the differential equation y''-16y=0  where c_1 and c_2 are arbitrary constants, find a function y(t) that satisfies the conditions

y'' - 16 y = 0

y(0)=6

lim t to inf+ ,y(t)=0

 

y(t)=?

Answer 1

THis question is similar (to some extent) to your previous one. You have a general solution and by using initial conditions you need to find a a particular solution.In other words, you need to specify (find) constants c1 abd C2. How? Just plug in the given solution into the DE and you will have a system of equations with two unknown C1 and C2. Solve for C1 and C2 and then put back their values into the solution. That's all. Try.