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Question: Answered & Verified by Expert
If $\frac{d y}{d x}=f(x, y)$ is a homogeneous differential equation, then the general form of $f(x, y)$ is
MathematicsDifferential EquationsAP EAMCETAP EAMCET 2023 (15 May Shift 1)
Options:
  • A $\mathrm{x}^{\mathrm{n}} \phi\left(\frac{\mathrm{y}}{\mathrm{x}}\right), \mathrm{n} \neq 1$
  • B $y^n \phi\left(\frac{x}{y}\right), n \neq 1$
  • C $\phi\left(\frac{y}{x}\right)$
  • D $\mathrm{K}^{\mathrm{n}} \mathrm{f}(\mathrm{x}, \mathrm{y}), \mathrm{n} \neq 1$
Solution:
1346 Upvotes Verified Answer
The correct answer is: $\phi\left(\frac{y}{x}\right)$
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. $\frac{d y}{d x}=f(x, y)=\phi(y / x)$

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