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!!