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AP EAMCET2010MathematicsDifferential Equations

The solution of y d y d x = (x+y)+ (x-y) is

Options

  1. Ay=2 x+c
  2. By=-2 x+c
  3. Cy=-2 x+c
  4. D^2 y=-2 x+c

Correct answer

B. y=-2 x+c

Step-by-step solution

y d y d x = (x+y)+ (x-y) y d y d x =2 ( 2 x 2 ) ( 2 y 2 ) [ C+ D=2 ( C+D 2 ) ( C-D 2 ) ] y d y d x =2 x y y y d y d x =2 x y On integrating y ^2 y d y= 2 x d x [ array l Let t= y d t d y =- y -d t= y d y array ] - d t t^2 =2(- x)+c - (- 1 t )=-2 x+c 1 y =-2 x+c y=-2 x+c

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