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COMEDK2014MathematicsDifferential Equations

The solution of (2 x-10 y³ ) d y d x +y=0 is

Options

  1. Ax y²=2 y⁵+C
  2. By x²=2 y⁵+C
  3. Cx² y²=2 y⁵+C
  4. DNone of these

Correct answer

A. x y²=2 y⁵+C

Step-by-step solution

Given, differential equation is aligned & (2 x-10 y³ ) d y d x +y=0 d y d x = -y 2 x-10 y³ & d x d y = 2 x-10 y³ -y = -2 x y +10 y² & d x d y + 2 y x=10 y² aligned Compare with linear differential equation d x d y +P x=Q IF =e^ 2 y d y =e^ y² =y² Required solution is x y²= 10 y² y² d y+C i.e. x y²=2 y⁵+C

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