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AP EAMCET2008MathematicsDifferential Equations

The solution of the differential equation d y d x = x-2 y+1 2 x-4 y is

Options

  1. A(x-2 y)^2+2 x=c
  2. B(x-2 y)^2+x=c
  3. C(x-2 y)+2 x^2=c
  4. D(x-2 y)+x^2=c

Correct answer

A. (x-2 y)^2+2 x=c

Step-by-step solution

Given that, d y d x = x-2 y+1 2 x-4 y Put x-2 y=z 1-2 d y d x = d z d x aligned & 1 2 [- d z d x +1 ]= z+1 2 z & - d z d x +1= z+1 z & d z d x =- 1 z & z d z=-d x & z^2 2 =-x+c₁ & (x-2 y)^2+2 x=c & aligned

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