C4 implict equation question help please!

y/x - 2x/y =1 where x>0 y>0

show that dy/dx = y/x

Tenchu

y/x - 2x/y =1 where x>0 y>0

show that dy/dx = y/x

Right this looks fairly tricky...

y/x - 2x/y = 1

So: [x(dy/dx) - y]/x² - [y(2) - 2x(dy/dx)]/y² = 0

[ use of the quotient rule twice ]

x(dy/dx)/x² - y/x² - 2y/y² + 2x(dy/dx)/y²

=> (dy/dx)[x^-1 + 2x/y²] = y/x² + 2y/y²

=> (dy/dx) = [y/x² + 2y^-1]/[x^-1 + 2x/y²]

=> dy/dx = [y(x^-2 + 2y^-2)] / [x(x^-2 + 2y^-2)]

=> dy/dx = y/x

I bet someone has beaten me to this one.

Reply 2

Sound Fondler

thanks man, it's all so clear now.

Reply 3

samd

Tenchu

thanks man, it's all so clear now.

lol. Not to me it isn't.

The implicit stuff is tough.

Reply 4

fabz

That was a horrible question! Where did you find it?

Reply 5

Sound Fondler

ye it is a tough question, worth 7 marks, it's from a C4 mock paper published by Delphis (the questions are harder than usual)

Reply 6

samd

Tenchu

ye it is a tough question, worth 7 marks, it's from a C4 mock paper published by Delphis (the questions are harder than usual)

Is there anyway that you could send the Delphis papers to me? Know of anywhere they are online etc?

I only have Solomon papers and I am running out fast. :eek: