Please answer the following question Let ydouble prime4yprim

Please answer the following question

Let y(double prime)-4y(prime) = 0

a) Try a solution of the form y = e^(rx), for ome unknow contant r, by substitutting it into the differential equation.

____________________= 0

b) Simplify and factor your equation in the previous part as much as possible. Be sure to divide out any terms guaranteed to be nonzero.

___________________=0

c) Find all values of r such that y = e^(rx) satisfied the differential equation. IF there is more than once correct answer, enter your answer as a comma seperated list.

______________________=0

Solution

y\'\' - 4y\' = 0

The auxialary equation is ,

r² - 4r = 0

r(r - 4) =0

r = 0 , r-4 = 0

r = 0 , r = 4

If the roots are real then the solution is ,

y = c₁e^rx + c₂e^rx

y = c₁e^0.x + c2e^4x

   y = c₁ + c₂e^4x