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Let y = y ( x ) be the solution of the differential equation (x y-5 x^2 1+x^2 ) d x+ (1+x^2 ) d y=0, y(0)=0 . Then y( 3 ) is equal to

Options

  1. A15 2
  2. B5 3 2
  3. C2 2
  4. D14 3

Correct answer

B. 5 3 2

Step-by-step solution

aligned & (1+x^2 ) d y d x +x y=5 x^2 1+x^2 & d y d x + x y 1+x^2 = 5 x^2 1+x^2 & I.F. = e ^ x 1+x^2 dx = e ^ (1+x^2 ) 2 = 1+ x ^2 & y 1+ x ^2 = 5 x ^2 1+ x ^2 1+ x ^2 dx & y 1+ x ^2 = 5 x ^2 1+ x ^2 1+ x ^2 dx & y 1+ x ^2 = 5 x ^3 3 + C & y (0)=0 0=0+ C C =0 aligned aligned & y= 5 x^3 3 1+x^2 & y( 3 )= 15 3 32 = 5 3 2 aligned

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