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AP EAMCET201921 Apr 2019Morning ShiftMathematicsDifferential EquationsActual

The solution of the equation d y d x +2 y x= x satisfying y=0 when x= 3 , is

Options

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

Correct answer

A. y=2 ^2 x+ x-2

Step-by-step solution

Given, differential equation is d y d x +2 y x= x Here, P=2 x and Q= x array ll & I . F=e^ 2 x d x & =e^ 2 | x| =e^ ^2 x = ^2 x array Now, required solution is, aligned & y I F= Q I F d x+c & y ^2 x= x ^2 x d x+c & y ^2 x= x x+c & y ^2 x= x+c aligned Given, y=0 when x= 3 aligned & 0=2+c & c=-2 & y ^2 x= x-2 aligned array ll & y= x ^2 x - 2 ^2 x & y= x-2 ^2 x & y= x-2 (1- ^2 x ) & y= x-2+2 ^2 x & y=2 ^2 x+ x-2 array

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