greeny93

given 5e^x - 4e^-x ≡A sinh x + B cosh x

Find A and B

skeeter

$5e^x-4e^{-x} = \dfrac{A(e^x - e^{-x})}{2} + \dfrac{B(e^x + e^{-x})}{2}$

$5e^x-4e^{-x} = \dfrac{(A+B)e^x + (B-A)e^{-x}}{2}$

$10e^x-8e^{-x} = (A+B)e^x + (B-A)e^{-x}$

$A+B = 10$

$B-A = -8$

can you finish?

greg1313

$$5e^x-4e^{-x}=8\sinh x+e^x=8\sinh x+ \sinh x+\cosh x=9\sinh x+\cosh x$$

greeny93

unfortunately not, more studying required on this topic i think

skeeter

come on ... it's basic algebra for solving a system of equations.

adding the last two equations term for term eliminates $A$ and yields the equation

$2B=2$

find $B$ and $A$ now?

greeny93

of course, i couldnt see the wood for the trees in that instance i had got myself so confused in the other questions i am doing, i had the answer for this one a long time ago, your method and stages really helped me so thank you