The first part of the problem is stated as:
Suppose h(x+1) = h(x) + h(x-1) and h(0) = 3 and h(1) = 12
With this information you can develop the definition of the function, h(x).
Regarding this part I did find a very similar problem as follows:
Suppose that h(x+1) = h(x) +h(x-1) and that h(0) = 3 and h(1)= 12. Find h(2), h(3) and h(-1)
This problem is solved using the known function values as follows:
h(1) = h(0) + h(-1)
12 = 3 + h(-1)
h(-1) = 9
h(2) = h(1) + h(0)
h(2) = 12 + 3
h(2) = 15
h(3) = h(2) + h(1)
h(3) = 15 + 12
h(3) = 27
But the second part of the problem as stated is:
Find: h(x) if 5h(x) = h(x) + x^2/h(x)
This appears to be unrelated to the first part and can be solved directly:
5h(x) = h(x) +x²/(h(x))
4h(x) = x²/(h(x))
4(h(x))² = x²
(h(x))² = x²/4
h(x) = ±x/2
