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Manipal MET2020MathematicsDifferential Equations

The solution of the differential equation a+x d y d x +x y=0 is

Options

  1. Ay=C e^ 2 3 (2 a-x) x+a
  2. By=C e^ 2 3 (a-x) x+a
  3. Cy=C e^ 2 3 (2 a+x) x+a
  4. Dy=C e^ - 2 3 (2 a-x) x+a

Correct answer

A. y=C e^ 2 3 (2 a-x) x+a

Step-by-step solution

Given differential equation is a+x d y d x +x y=0 a+x d y d x =-x y d y y = -x a+x d x On integrating both sides, we get y- C= [ -x-a a+x + a a+x ] d x ( y C )=- x+a d x+a 1 a+x d x=- (x+a)^ 3 / 2 3 / 2 +a (a+x)^ 1 / 2 1 / 2 array rlrl & & = 2 3 (2 a-x) x+a & & y C & =e^ 2 3 (2 a-x) x+a & y & =C e^ 2 3 (2 a-x) x+a array which is the required solution.

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