Which of the following functions arc solutions of the differ

Which of the following functions arc solutions of the differential equation y\" - 6y\'+ 9y = O? y(x) = 3xe3x y(x) = 3x y(x) = x2e3x y(x) = e-3x y(x) =0 y(x) = xe3x y(x) = e3x

Solution

Writing auxillary equation
x^2-6x+9=0
roots of this equation are equal and are 3,3
so general solution of this equation is
c1*e^3x+c2*x*e^3x

where c1 and c2 are constants

for option A put c1=0 and c2=3

for E put c1=c2=0

for F c1=0 and c2=1

for G c1=1 and c2=0

=> A, E, F and G are the solution