# Integration?

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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?

• Integration? -

if y=Ake^kx then

Ake^kx -3Ae^kx=4e^2x

dividing by e^kx

Ak-3A=4(e^(2x-kx))

If A,k are constants, then the exponential term has to go to zero (Ak-3A) has to equal a constant...

or k=2 to do that, then
2A-3A=4 which solves A

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