Find the GS of the following DE y 3y 18y 0SolutionWe have

Find the G.S. of the following DE: y\" - 3y\' - 18y = 0

Solution

We have a linear homogeneous equation with constant coefficients

So solution is of the form:y=exp(kx)

Substituting gives

k^2-3k-18=0

k^2-6k+3k-18=0

k=-3,6

So genreal solutin is

y=Ae^{-3x}+Be^{6x}