I’m having a bit of difficulty obtaining the answer given at the back of my paper.
Here is the problem:
(d^2y/dt^2) – ( 6dy / dt ) + 8y = 0
our initial conditions:
y(0) = 1
y'(0) = 0
working:
-> m^2 – 6m + 8 = 0
put into formula:
m = (-b +- squareroot( b^2 – (4)ac)) / 2a
working:
-> m = 6 +- squareroot( -6^2 – (4)(1)^2(8)) / (2)(1)
-> m = (6 +- squareroot( 36 – 32)) / 2
Can now identify the nature of our roots, which is Distinct so we’re using this formula (k1 is a constant):
y(t) = K1e^(m1t) + k2e^(m2t)
now continue our working from above to find m1 and m2:
-> (m = 6 + squareroot(4)) / 2
-> m1 = 4
-> m2 = 2
put m1 and m2 into the formula:
y(t) = k1e^(4t) + k2e^(2t)
Now this is the part that I don’t understand. We now have to find the constants and all the answer in the book gives is:
y(0) k1 + k2 = 1
y'(0) = 2k1 + 4k2 = 0
solving: y(t) = 2e^(2t) – e^(4t)
Can someone explain how I get to this part with working please?
0 comments