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AP EAMCET201822 Apr 2018Evening ShiftMathematicsDifferential EquationsActual

The general solution of d y d x +y x=2 x+x^2 x

Options

  1. Ay-x^2=c x
  2. By x=x^2 x+c
  3. Cy x=x^2+c x
  4. Dy=x^2+c x

Correct answer

D. y=x^2+c x

Step-by-step solution

Given differential equation, The differential equation is in linear form, so Integrating factor (I.F.) =e^ x d x = x So, solution of given differential Eq. (i), is aligned y( x) & = (2 x+x^2 x ) x d x & = 2 x x d x+ x^2 x x d x & = 2 x x d x+x^2 x- 2 x x d x y x & =x^2 x+c y & =x^2+c x . aligned

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