Question

find a Differential equation for the family of this curve... cy^2+4y=2x^2 c=constant

Answer 1

see if you can use implicit differentiation on it and solve for y'

Answer 2

what the procedure last time I diferentieted implicitly was last year

Answer 3

f(y) -> f'(y) * y'
eg. d/dx (4y^3) = 12y^2 *y'

Answer 4

f(x) -> f'(x) (as usual)
eg. d/dx (x^3) = 3x^2

Answer 5

ow jah I tried dat but I do not get the given answer..

Answer 6

what was the final answer?

Answer 7

it's suppose to be(x^2-y)y'=xy

Answer 8

hmh, let me look it over a bit...

Answer 9

ah, I think we have to use partials..

Answer 10

\[2cyy^'+4y^'=4x\]
\[y ^{'}=\frac{ 2x }{ cy+2}\]

Answer 11

jonask can u change yr answer to the 1 I gave?

Answer 12

coz u dd exactly wat i dd....jst tht the answr do not dorrespond!

Answer 13

I think I messed up @ekim2012 , but I found the right procedure and I'm looking it over. Just a moment..

Answer 14

cul

Answer 15

i divided by 2
\[cyy^'+2y^'=2x\]
factorise then
\[y^'(cy+2)=2x\]

Answer 16

no..not coreect answer!!!!:)

Answer 17

you sure you're on the right solution @ekim2012 ? I did it the other way and got the same result as using implicit diff.

Answer 18

yes..but it's fine unkess they wrote the wrong solution..but I dn't thnk so!!

Answer 19

Are you sure you gave the right eqn. ?

Answer 20

you can also solve for x\[x^2=cy^2+4y\]
\[x=(cy^2+4y)^{1/2}\]
\[\frac{ dx }{ dy }=\frac{ 1/2(2cy+4) }{ \sqrt{cy^2+4y} }=\frac{ cy+2 }{\sqrt{cy^2+4} }\]

Answer 21

4y inside,to find dy/dx you can invert

Answer 22

is the solution only in terms of x

Answer 23

k..I'll just ask my lecturer tommorow nd report to u guys...yes it's only in terms of x...here is it (x^2-y)y'=xy

Answer 24

Sorry, @ekim2012 ! It's possible that I'm thinking about this incorrectly...

Answer 25

fine....

Answer 26

http://www.wolframalpha.com/input/?i=simplify+%282x^2+-+4y%29%2F%28y^2%29+2y+y%27+%2B+4y%27+%3D+4x

Answer 27

Thanks experiment....u gud