# Plz solve this my frnds its quite urgent

1
by vivek2001

2015-02-15T23:19:17+05:30

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I dont know the best way of solving this.  I am able to solve it in the following manner.

y - x  y'  =  x + y  y'
(x + y)  y' =  y - x       --- equation (1)

Let  y = g x          =>            y' = g + x g'

Substitute in equation (1),
x g + x² g' + x g² + x² g g' =  g x - x
x g' (1 + g) = - (g² + 1)

- 1/x = (g + 1) g' / (g² + 1)
-1/ x  =  g g' / (g² + 1)  +  g' / (g² + 1)
Integrating we get,
Ln 1/x  + Ln K  =  1/2 Ln (1 + g²)  +  tan⁻¹ g
Substitute g = y/x, and simplify.

You may verify the solution, by differentiating this equation and obtaining the expression for y'.

thank u sir but isn't there easier way????