Question

Solve the differential equation y" + 4y' + 5 = 0

Answer 1

let y=e^(mx) be the trial sol.
then y'' = m^2* e^(mx) and y'= m*e^(mx)
putting these in the eq. we have the auxillary sol. as
m^2+4m +5= 0
(m+2)^2+1=0
hence m= -2 +i,-2-i
hence the reqd sol. is y=e^(-2x)(Acosx+Bsinx) where A and B are constants