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The equation of the curve passing through the origin and satisfying the differential equation (1+x^2 ) d y d x +2 x y=4 x^2 is

Options

  1. A(1+x^2 ) y=x^3
  2. B3 (1+x^2 ) y=2 x^3
  3. C(1+x^2 ) y=3 x^3
  4. D3 (1+x^2 ) y=4 x^3

Correct answer

D. 3 (1+x^2 ) y=4 x^3

Step-by-step solution

Given differential equation is aligned & (1+x^2 ) d y d x +2 x y=4 x^2 & d y d x + ( 2 x 1+x^2 ) y= 4 x^2 1+x^2 aligned This is linear diff. equation I . F =e^ 2 x 1+x^2 d x =e^ (1+x^2 ) =1+x^2 Solution is aligned &y (1+x^2 )= 4 x^2 1+x^2 1+x^2+ C & y (1+x^2 )= 4 x^3 3 + C & Required curve is &3 y (1+x^2 )=4 x^3( C =0) aligned

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