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MHT CET202124 Sep 2021Morning ShiftMathematicsDifferential EquationsActual

The particular solution of the differential equation y(1+ x) d x d y -x x=0 when x=e, y=e^2 is

Options

  1. Ay^2=e^4 x
  2. By=e^2 x
  3. Cy=x^2 x
  4. Dy=e x x

Correct answer

D. y=e x x

Step-by-step solution

aligned & y(1+ x) d y d x -x x=0 & y(1+ x) d y d x =x x d y d x = y(1+ x) x x & d y d x = 1+ x x x d x & |y|+ |x x|+ c & We have x=e, y=e^2 & |e|^2= |e e|+ c & 2=1+ c c=1= e & |y|= |x x|+ e & y=e x x aligned

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