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AP EAMCET202017 Sep 2020Evening ShiftMathematicsDifferential EquationsActual

The integrating factor of (x d y d x +3 y=x^2 ) is

Options

  1. A( 3 x )
  2. B( x )
  3. C(x^3 )
  4. D(x )

Correct answer

C. (x^3 )

Step-by-step solution

Given equation is, (x d y d x +3 y=x^2 or d y d x + 3 x y=x ) Comparing with, ( d y d x +P y=Q, ) We have (p= 3 x ) and So, the integrating factor is, ( IF =e^ p d x =e^ 3 x d x =e^ 3 x =e^ x^3 =x^3 ) (r= d^ 2 = 0.8 2 =0.4 ~mm =4 10⁻⁴ ~m ) Hence, ( l= m g l r^2 Y = 10 10 3 (4 10⁻⁴ )^2 10¹¹ ) (=5.96 10⁻³ ~m =0.596 ~cm 0.6 ~cm )

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