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AP EAMCET202421 May 2024Evening ShiftMathematicsDifferential EquationsActual

If x d y d x -y x=6 x, (0 x, 2 ) and y ( 3 )=0 then y ( 6 )=

Options

  1. A- ^2 4 3
  2. B- ^2 2
  3. C- ^2 2 3
  4. D^2 2 3

Correct answer

C. - ^2 2 3

Step-by-step solution

aligned & x d y d x -y x=6 x d(y x)=6 x d x & y x=3 x^2+C & y ( 3 )=0 0= ^2 3 +C C= - ^2 3 & y x=3 x^2- ^2 3 . Now, at x= 6 & y ( 6 ) 3 2 = ^2 12 - ^2 3 = - ^2 4 y ( 6 )= - ^2 2 3 aligned

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