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AP EAMCET2013MathematicsDifferential Equations

The solution of the differential equation d y d x -2 y 2 x=e^x 2 x is

Options

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

Correct answer

B. y 2 x=e^x+C

Step-by-step solution

Given, differential equation is d y d x -2 y 2 x=e^x 2 x Here, P=2 2 x, Q=e^x 2 x aligned IF & =e^ -2 2 x d x & =e^ -2 2 x 2 & =e^ - 2 x & = 1 2 x aligned Required solution is aligned & y 2 x = e^x 1 2 x 2 x d x+C y 2 x & = e^x 1 d x+C & y 2 x=e^x+C aligned where, C is the constant of integration.

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