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MHT CET202120 Sep 2021Morning ShiftMathematicsDifferential EquationsActual

The general solution of the differential equation x+y d y d x = (x^2+y^2 ) is

Options

  1. A(x^2+y^2 )=2 x+c
  2. B(x^2+y^2 )+2 x=c
  3. C(x^2+y^2 )+x=c
  4. D(x^2+y^2 )=2 x+c

Correct answer

A. (x^2+y^2 )=2 x+c

Step-by-step solution

aligned & We have, x+y d y d x = (x^2+y^2 ) & Put x^2+y^2=u 2 x+2 y d y d x = d u d x & x+y d y d x = 1 2 d u d x & 1 2 d u d x = u & d u u = 2 d x & u=2 x+c & (x^2+y^2 )=2 x+c aligned

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