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AP EAMCET · Maths · Differential Equations

The general solution of the differential equation \(\frac{d y}{d x}=\frac{2 x+y-3}{2 y-x+3}\) is

  1. A \(x^2-x y-y^2+3 x+3 y+c=0\)
  2. B \(x^2-x y-y^2-3 x-3 y+c=0\)
  3. C \(x^2+x y-y^2-3 x-3 y+c=0\)
  4. D \(x^2+x y+y^2+3 x-3 y+c=0\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(x^2+x y-y^2-3 x-3 y+c=0\)

Step-by-step Solution

Detailed explanation

\((2x+y-3)dx - (2y-x+3)dy = 0 \implies (2x+y-3)dx + (x-2y-3)dy = 0\). \(M = 2x+y-3\), \(N = x-2y-3\). \(\frac{\partial M}{\partial y} = 1\), \(\frac{\partial N}{\partial x} = 1\). Since \(\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}\), the equation is exact.…