Find The General Solution Of The Differential Equation Dy/Dx - Y/X = 0.

Sol:

Given:

[latex]\frac{dx}{dy} – \frac{x}{y} = 0[/latex] [latex]\Rightarrow \frac{dy}{dx} = \frac{x}{y}\\\Rightarrow \frac{dy}{y} = \frac{dx}{x}.[/latex]

Integrating both sides, log y = log x + c where c is an arbitrary constant.

[latex]\Rightarrow[/latex] log y = log kx

where k is greater than zero.

[latex]\Rightarrow[/latex] y = kx

Therefore, the general solution of the differential equation

[latex] \frac{dx}{dy} – \frac{x}{y} [/latex]= 0 is y = kx

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