Integration?
posted by Aoi on .
given that y=Ae^kx, where A and k are constants, find an expression for dy/dx. Hence find the value of k and of A for which dy/dx  3y = 4e^2x
okay, i know the first part is dy/dx=Ake^kx
but how do i do the second part? find A and k?

if y=Ake^kx then
Ake^kx 3Ae^kx=4e^2x
dividing by e^kx
Ak3A=4(e^(2xkx))
If A,k are constants, then the exponential term has to go to zero (Ak3A) has to equal a constant...
or k=2 to do that, then
2A3A=4 which solves A