Find the function satisfying the differential equation y5y3e

Find the function satisfying the differential equation

y??5y=3e^(6t)

and y(0)=?2

y??5y=3e^6t

dy/dx - 5y = 3e^6t

so,

IF = e^int p(x) dx

IF = e^int (-5dx)

IF = e^(-5x)

y(IF) = int (IF * q(x) dx)

ye^(-5x) = int (e^(-5x) * 3e^(6x) dx)

ye^(-5x) = 3 int (e^x dx)

y e^(-5x) = 3e^x + c

y = 3e^6x + c*e^5x

y(0) = -2

-2 = 3*1+c*1

c = -5

So,

y = 3e^6x - 5*e^5x