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MHT CET202122 Sep 2021Morning ShiftMathematicsDifferential EquationsActual

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

Options

  1. A2 ex x-y=e^2
  2. B3 e x y x-y=2 e^2
  3. Ce x x+y=2 e^2
  4. De x x-y=0

Correct answer

D. e x x-y=0

Step-by-step solution

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

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