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BITSAT2022MathematicsDifferential EquationsActual

( d y d x ) x=y ^2 x+ x , find general solution

Options

  1. Ay= x( | cosec x- x|+ x+c)
  2. By= ^2 x+ x+c
  3. Cy= | x+ x|+ cosec x+c
  4. Dy= ^2 x+ x+c

Correct answer

A. y= x( | cosec x- x|+ x+c)

Step-by-step solution

Given that aligned & ( d y d x ) x=y ^2 x+ x & x ( d y d x )-y ^2 x= x & d y d x + ( - ^2 x x ) y= x x & Here, P=- ^2 x x and Q= x & IF =e^ P d x =e^ - ^ 2 x x d x & IF =e^ - ( x) =e^ x = x & Now, y IF = (Q IF ) d x+C & y x= x x+C & y x= 1- ^2 x x +C & y x= | cosec x- x|+ x+C aligned

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