1. ## I just had one class of differential equations and a huge homework about it

IF dy/dx= squareroot(x/y) and y=4 then x=1, what is the equation y?

2. ## Re: I just had one class of differential equations and a huge homework about it

Originally Posted by emilyastrid
IF dy/dx= squareroot(x/y) and y=4 then x=1, y =???
You just told us that $y=4$. Now you want to know what y is equal to? It is still 4.

3. ## Re: I just had one class of differential equations and a huge homework about it

i meant the equation y.

4. ## Re: I just had one class of differential equations and a huge homework about it

Originally Posted by emilyastrid
i meant the equation y.
You have

$$\dfrac{dy}{dx} = \sqrt{\dfrac{x}{y}}$$

Multiplying out gives:

$$\sqrt{y}dy = \sqrt{x}dx$$

You can rewrite as:

$$y^{1/2}dy = x^{1/2}dx$$

Now, integrate both sides. Plug in $(1,4)$ to determine the constant of integration. Solve for $y$.

5. ## Re: I just had one class of differential equations and a huge homework about it

Originally Posted by emilyastrid
IF dy/dx= squareroot(x/y) and y=4 then x=1, what is the equation y?
You have a typo- you meant to say "y= 4 when x= 1" or, more simply, "y(1)= 4".