Find the special solution of the differential equation 4Y "- 12Y '+ 9y = 0 satisfying the initial conditions y ▏ y = 0 = 1, y' ▏ x = 0 = 1 The comma above is an apostrophe

Find the special solution of the differential equation 4Y "- 12Y '+ 9y = 0 satisfying the initial conditions y ▏ y = 0 = 1, y' ▏ x = 0 = 1 The comma above is an apostrophe

The characteristic equation is 4R ^ 2-12r + 9 = 0, r = 3 / 2
So y = e ^ (3x / 2) (c1x + C2)
y'=e^(3x/2)(3C1/2*x+3C2/2+C1)
Let x = 0
1=C2,1=3C2/2+C1
The solution is C1 = - 1 / 2, C2 = 1
So y = e ^ (3x / 2) (- X / 2 + 1)