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AP EAMCET202418 May 2024Morning ShiftMathematicsDifferential EquationsActual

The general solution of the differential equation ( y ^2 y-x ^2 y ) d y=( y) d x is

Options

  1. Ay=3 x ^3 y+c
  2. Bx( y+ y)= ^2 y+c
  3. Cy y=x^2 ^2 y+c
  4. D3 x y+ ^3 y=c

Correct answer

D. 3 x y+ ^3 y=c

Step-by-step solution

Given, differential equation ( y ^2 y-x ^2 y ) d y= y d x d x d y + x ^2 y y = ^3 y So, I.F. =e^ ^2 y y d y =e^ ( y) = y So, solution is given by x y= ^3 y y d y= ^2 y y d y x y=- ^3 y 3 + C ₁ 3 x y+ ^3 y= C

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