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AP EAMCET · Maths · Differential Equations

If \(\frac{d y}{d x}=f(x, y)\) is a homogeneous differential equation, then the general form of \(f(x, y)\) is

  1. A \(\mathrm{x}^{\mathrm{n}} \phi\left(\frac{\mathrm{y}}{\mathrm{x}}\right), \mathrm{n} \neq 1\)
  2. B \(y^n \phi\left(\frac{x}{y}\right), n \neq 1\)
  3. C \(\phi\left(\frac{y}{x}\right)\)
  4. D \(\mathrm{K}^{\mathrm{n}} \mathrm{f}(\mathrm{x}, \mathrm{y}), \mathrm{n} \neq 1\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\phi\left(\frac{y}{x}\right)\)

Step-by-step Solution

Detailed explanation

Since \(\frac{d y}{d x}=f(x, y)\) is said to be a homogeneous differential equation if \(\mathrm{f}(x, y)\) is a homogenous function of degree zero. i.e. \(\frac{d y}{d x}=f(x, y)=\phi(y / x)\)