How do you solve 40000y''-729y=0?

Question

Please show steps for this solution. Thanks!

Answer 1

How do you solve 40000y''-729y=0?

Assume a solution to the homogeneous equation of the form, y = e^(mx).

Then y = m.e^(mx),   y'' = m^2.e^(mx)

The DE now is,

40000.m^2.e^(mx) - 729.e^(mx) = 0

200^2.m^2.e^(mx) - 27^2.e^(mx) = 0

200^2.m^2 = 27^2

m = +/- 27/200

The solution now is: y = A.e^(27x/200) + B.e^(-27x/200)