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MHT CET202312 May 2023Morning ShiftMathematicsDifferential EquationsActual

The differential equation (x+y) d y= d x has the general solution given by

Options

  1. Ay= (x+y)+ c , where c is a constant.
  2. By= (x+y)+ c , where c is a constant
  3. Cy= ( x+y 2 )+ c , where c is a constant
  4. Dy= 1 2 (x+y)+ c , where c is a constant

Correct answer

C. y= ( x+y 2 )+ c , where c is a constant

Step-by-step solution

aligned & (x+y) d y= d x & d x ~d y = (x+y) aligned Put x+y= u Differentiating w.r.t. y , we get d x ~d y +1= du d y d x ~d y = du d y -1 Substituting (ii) and (iii) in (i), we get aligned & du d y -1= u & du 1+ cosu = d y & du 2 ^2 ( u 2 ) = d y aligned Integrating on both sides, we get aligned & 1 2 ^2 ( u 2 ) du = d y & y= ( x+y 2 )+ c aligned

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