Q119 / 160 · AP EAMCET 2023 (15 May Shift 1) · Mathematics

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

  • A
    $\mathrm{x}^{\mathrm{n}} \phi\left(\frac{\mathrm{y}}{\mathrm{x}}\right), \mathrm{n} \neq 1$
  • B
    $y^n \phi\left(\frac{x}{y}\right), n \neq 1$
  • Correct answer
    C
    $\phi\left(\frac{y}{x}\right)$
  • D
    $\mathrm{K}^{\mathrm{n}} \mathrm{f}(\mathrm{x}, \mathrm{y}), \mathrm{n} \neq 1$

Solution

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. $\frac{d y}{d x}=f(x, y)=\phi(y / x)$

Hence, the correct answer is option: 'C'.

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