Question

*Solve the differential equation dy/dx=x/16y.
*Find the equation of the solution through the point (x,y)=(−4,1).
*Find the equation of the solution through the point (x,y)=(0,−4). Your answer should be of the form y=f(x)

Answer 1

I already solved the first part.
C=8y^2 -(x^2/2)

Answer 2

ok replace your x and y with -4 and 1 respectively to find the C so that your graph for your equation will go through that point

Answer 3

so y=sqrt((x^2/16) + c) and i plugged in (-4,1) and got y=sqrt((x^2/16)
is that correct?

Answer 4

c= 0 for the second question?

Answer 5

You have \[C=8y^2-\frac{x^2}{2}\]
Replace x with -4 and y with 1 like this:
\[C=8(1)^2-\frac{(-4)^2}{2}\]
Is this what you did to solve for C?

Answer 6

\[C=8-\frac{16}{2}=8-8=0\]

Answer 7

yes that's what i did

Answer 8

I can't do arithmetic somethings lol
But you have \[0=8y^2-\frac{x^2}{2} \]

Answer 9

that is the equation satisfying the point (-4,1)

Answer 10

hmm it the system doesn't seem to accept it.. it says it isn't a linear equation

Answer 11

doesn't that mean i have to solve for y=...

Answer 12

Your differential equation was:
\[\frac{dy}{dx}=\frac{x}{16y} \text{ \right ?} \]

Answer 13

yup

Answer 14

Ok solve for y
make sure you keep in mind we want to go through the point (-4,1)

Answer 15

ok so y=x/4

Answer 16

but it still doesn't work??

Answer 17

oh wait y=-x/4 works!!

Answer 18

We wanted y=-x/4
That is why I said to keep in mine we want it going through (-4,1) :)

Answer 19

mind*

Answer 20

The equation y=x/4 doesn't satisfy the point (-4,1)
but y=-x/4 does

Answer 21

Like 1=-(-4)/4

Answer 22

ohh i get it now

Answer 23

thanks a lot!!

Answer 24

i'm going to do the last part now

Answer 25

c=128 for the last part right?

Answer 26

oh i got the last part too!!

Answer 27

thanks a lot again!!!

Answer 28

yes C=128 for the last one