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MHT CET20225 Aug 2022Morning ShiftMathematicsDifferential EquationsActual

A curve passes through the point (1, 6 ) . Let the slope of the curve at each point (x, y) be given by y x + ( y x ), x>0 , then the equation of the curve is

Options

  1. A( y x )= x+ 1 2
  2. Bcosec ( y x )= e+2
  3. C( 2 y x )= x+ 1 2
  4. D( 2 y x )= x+2

Correct answer

A. ( y x )= x+ 1 2

Step-by-step solution

Here dy dx = y x + ( y x ) Let y x =v y=v x d y d x =v+x d v d x aligned & v+x d v d x =v+ v & x d v d x = secv & v d v= d x x & sinv = _e x+C aligned ( y x )= _e x+C Putting x =1, y = 6 c = 1 2 ( y x )= _e^x+ 1 2

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