1. ## differential equations

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!!

2. Originally Posted by littlejodo
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
That is not correct, because

4y = x

y = x /4

Integrate

1/2 *y^2 = 1/2 * x^2 /4

multiplied by 2

y^2 = x^2/4

not! y^2 = x^2

3. okay, thanks!

so then y = sqrt(x^2/4) or sqrt(x^2) / sqrt(4) which is +/- x/2

since when x = 4, y = 5, the equation needs to be
y = x/2 + 3 ( or that is what I would think, but it is wrong)

what did I do wrong now?

4. ## solved

I got it. I have a bad habit of leaving off the constant until the end.

thanks!!!