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JEE Main2012MathematicsDifferential EquationsActual

The general solution of the differential equation d y d x + 2 x y=x^2 is

Options

  1. Ay=c x⁻³- x^2 4
  2. By=c x^3- x^2 4
  3. Cy=c x^2+ x^3 5
  4. Dy=c x⁻²+ x^3 5

Correct answer

D. y=c x⁻²+ x^3 5

Step-by-step solution

Given differential equation is d y d x + 2 x y=x^2 This is of the linear form. aligned & P= 2 x , Q=x^2 & I.F =e^ 2 x d x =e^ x^2 =x^2 aligned Solution is aligned & y x^2= x^2 x^2 d x+c= x^5 5 +c & y= x^3 5 +c x⁻² aligned

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