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Guest
Guest
Hi there, I'm doing some revision for a test, and have come across a question on last years paper which has me stumped somewhat, so here it is, along with my working do far;
[dy/dx]= (y^2 + x^2)/(x*y + x^2)
So first I divided top and bottom by x^2, then made the substitution v=y/x to get...
[dy/dx]= (v^2 + 1)/(v + 1)
And we know from the chain rule applied to v=y/x; [dy/dx]= v + x[dv/dx]
And so...
v + x[dv/dx]= (v^2 + 1)/(v+1)
With a little re-arranging...
x[dv/dx]= (1 - v)/(1 + v)
So seperate the variable and integrate, ok so far?
But it's the integration I'm struggling with, I don't see an easy way of integrating (1 - v)/(1 + v) easily?! Am I making things too complicated for myself or something?
Any help or pointers on where I've gone/going wrong are much appreciated.
Cheers
Josh
[dy/dx]= (y^2 + x^2)/(x*y + x^2)
So first I divided top and bottom by x^2, then made the substitution v=y/x to get...
[dy/dx]= (v^2 + 1)/(v + 1)
And we know from the chain rule applied to v=y/x; [dy/dx]= v + x[dv/dx]
And so...
v + x[dv/dx]= (v^2 + 1)/(v+1)
With a little re-arranging...
x[dv/dx]= (1 - v)/(1 + v)
So seperate the variable and integrate, ok so far?
But it's the integration I'm struggling with, I don't see an easy way of integrating (1 - v)/(1 + v) easily?! Am I making things too complicated for myself or something?
Any help or pointers on where I've gone/going wrong are much appreciated.
Cheers
Josh