Stuck on separable equation (algebra prob?)

[darryw]

stuck on separable equation (algebra prob??)

Homework Statement

y' = 2x/(1+2y) y(2) = 0

(1+2y)dy = 2xdx

integrate both sides

y + y^2 = x^2 + c

I am stuck trying to put in in explicit form, so y = ...

is this completing the square or something?

Homework Equations

The Attempt at a Solution

 

[Dick]

First find c. Then, sure, if you want to solve for y(x) then complete the square.

 

[darryw]

c = y + y^2 - x^2

c = 0 + 0^2 - (2^2)

c = 4

y + y^2 = x^2 + 4

But i still don't see how complteting square will pu equation into form y = ... ?

 

[Dick]

c=4 doesn't work. 0 isn't equal to 2^2+4. Can you fix that? Why don't you complete the square in y before you decide it doesn't work?

 

[darryw]

should be -4

c = y + y^2 - x^2

c = 0 + 0^2 - (2^2)

c = -4

y + y^2 = x^2 - 4

COmpleting square is confusing me. How does that help with a DE? It is used to find the roots, but I am trying to get the equation to look like: y = something
thank you

 

[Dick]

You are trying to find the roots. You are trying to solve for y. Can you write y+y^2 in the form (y+A)^2-B by finding the constants A and B? Wouldn't that help to solve for y?

 

[darryw]

How do i get the equation y + y^2 = x^2 - 4 into the form y= ...

the answer key uses the quadratic formula but I am confused what a, b and c would be in the equation. ( -b +/- root b^2 - 4ac / 2a)

i can rearrange so that its: y^2 + y - x^2 + 4 = 0,

and i can see that a must be "1" .. but what is b and c when equation is in this form??

 

[Dick]

How do i get the equation y + y^2 = x^2 - 4 into the form y= ...

the answer key uses the quadratic formula but I am confused what a, b and c would be in the equation. ( -b +/- root b^2 - 4ac / 2a)

i can rearrange so that its: y^2 + y - x^2 + 4 = 0,

and i can see that a must be "1" .. but what is b and c when equation is in this form??

b=1 (since it's the coefficient of the y) and c=(-x^2+4) (since it's the 'constant' part independent of y).