I have a function of the form:
y:= x-> ((1 + ax + bx^2)/(1 + cx + dx^2))*(ln(sinh(x)^2 + cosh(x)^2)
I would like to know how I could use Maple to calculate the values that the constants a,b,c and d should take such that the expansion of the above function does not include powers of the order x^3, x^4, x^5 or x^6 ie. such that the powers are quadratic at most.
The trigonometric terms just to clarify are the square terms ie. sinh(x) * sinh(x), but that is how I have written them before with Maple. Not sure if I have written it out correctly, but it is a fraction with the constants multiplying the natural log function whose argument is the sum of the squares of the hyperbolic trigonometric functions.