y prime = 4x\y and x = -1 when y = 4. What can x be when y = 6?

Question

anonymous · Answer

$$y \prime = \frac{ 4x }{ y }$$

anonymous · Answer

$$\begin{array}{rcl}
y' &=& \frac{4x}{y} \
yy' &=& 4x \
\int yy' dx &=& \int 4x dx &\text{note: } & dy = y'dx \
\int y dy &=& \int 4xdx \
\frac{y^2}{2} +C_1 &=& \frac{4x^2}{2} + C_2 \
y^2 &=& 4x^2 + C 
\end{array}$$

anonymous · Answer

This is just a separable equation.

anonymous · Answer

Hmm, that's interesting, the multiple choice answers to this problem are:
A -6
B -sqrt 6
C -2
D 2
E 6

Is there a way to get it down to x = ?

anonymous · Answer

Well, sure you can get it into the form $x=?$ , but you need to solve for $C$ first.

anonymous · Answer

Some algebra tells you: $$
x = \pm \sqrt{\frac{y^2-C}{4}}
$$
So not only do you have to solve for $C$, but you need to figure out if the $\pm$ is a $+$ or a $-$.

anonymous · Answer

The tell you $x = -1$ when $y = 4$, so try substituting that in to find these things out.

anonymous · Answer

@thepro242   Do I really have to do the algebra for you too?  
You should have mastered that stuff by now

anonymous · Answer

No, sorry I got confused on what the next step was. Thank you for the help.

anonymous · Answer

ohh my, I was being dumb