Find the solution to the differential equation y 11y 18y

Solution

general formula

D²-11D+18=0

(D-9)(D-2)=0

D=2,9

y=C₁e^2t+C₂e^9t

y(0)=3=C₁+C₂

y\'=2C₁e^2t+9C₂e^9t

y\'(0)=1=2C₁+9C₂

Thus,

C₁=26/7

C₂=-5/7

y=(26/7)e^2t-(5/7)e^9t