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COMEDK2023MathematicsDifferential Equations

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

Options

  1. Ax=-2 y+C
  2. By=2 y+C
  3. Cy=-2 x+C
  4. Dx=-2 y+C

Correct answer

C. y=-2 x+C

Step-by-step solution

Given, differential equation is aligned & ( d y d x ) y= (x+y)+ (x-y) & ( d y d x ) y=2 ( x+y+x-y 2 ) & ( d y d x ) y y =2 x y & y ^2 y d y=2 x d x aligned On integration both sides, we get aligned & y ^2 y d y= 2 x d x & - ( y)⁻²⁺¹ (-2+1) =-2 x+C & 1 y =-2 x+C y=-2 x+C aligned

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