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AP EAMCET2006MathematicsDifferential Equations

The solution of d x d y + x y =x^2 is :

Options

  1. A1 y =c x-x x
  2. B1 x =c y-y y
  3. C1 x =c x+x y
  4. D1 y =c x-y x

Correct answer

B. 1 x =c y-y y

Step-by-step solution

d x d y + x y =x^2 1 x^2 d x d y + 1 x y =1 Put 1 x =t - 1 x^2 d x d y = d t d y - d t d y + t y =1 d t d y - t y =-1 On comparing with d y d x +P y=Q , we get P=- 1 y , Q=-1 I. F. =e^ P d x =e^ - 1 y d y = 1 y The solution is t( I. F. )= Q (I. F. ) d y+ct 1 y = (-1) 1 y d y+c 1 x 1 y =- y+c 1 x =c y-y y

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