If frac{dy}{dx} = f(x, y) is a homogeneous di | vedclass

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(C) differential equation of the form $\frac{dy}{dx} = f(x, y)$ is said to be a homogeneous differential equation if the function $f(x, y)$ is a homog

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

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(C) differential equation of the form $\frac{dy}{dx} = f(x, y)$ is said to be a homogeneous differential equation if the function $f(x, y)$ is a homogeneous function of degree zero. By definition,a function $f(x, y)$ is homogeneous of degree zero if $f(\lambda x, \lambda y) = \lambda^0 f(x, y) = f(x, y)$. Such a function can always be expressed in the form $f(x, y) = \phi\left(\frac{y}{x}\right)$ or $f(x, y) = \psi\left(\frac{x}{y}\right)$. Therefore,the general form of $f(x, y)$ for a homogeneous differential equation $\frac{dy}{dx} = f(x, y)$ is $\phi\left(\frac{y}{x}\right)$.

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

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