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The curve satisfying the eqn dy / dx = (y 2 - 2xy - x 2 ) / (y 2 + 2xy - x 2 ) passes through (-1, 1) is a (a) staight line (b) circle (c) ellipse (d) none of these

The curve satisfying the eqn 


dy / dx = (y2 - 2xy - x2) / (y2 + 2xy - x2)    passes through (-1, 1) is a 


(a) staight line      (b) circle    (c) ellipse     (d) none of these

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

Dear Sanchit Gupta

dy / dx = (y2 - 2xy - x2) / (y2 + 2xy - x2)

Let y=vx

dy/dx =v+xdv/dx

 

so v+x dy/dx =(v2 - 2v -1) / (v2 + 2v - 1)

x dv/dx =(v2 - 2v -1) / (v2 + 2v - 1)     -v

x dv/dx = -(v3 +v2 +v +1)/(v2 + 2v - 1)

(v2 + 2v - 1)/(v3 +v2 +v +1)  dv =-dx/x

 

Now variable are seperated you can solve the differential equation


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