Find a function y of x such that 4yy'= x and y(4) = 5

y = ? (function of x)

I approached this problems in the same way as other differential equations but have not arrived at a correct answer. I was treating y' the same as dy/dx and if this is incorrect, how and why?

Since the variables are already separated, I integrated both sides:

4y = x

4y^2/2 = x^2/2

2y^2 = x^2/2

Then I solved for y:

y^2 = (x^2/2) / 2

y^2 = x^2

y = +/- x + C

since when x = 4, y = 5

y = x + 1 or y = x+9

neither of these equations are correct. Please help me figure out where I went wrong! I am new to these types of problems and my book doesn't have any examples using the y' notation so I'm not sure exactly how to approach it.

Thanks!!