Aspire Faculty ID #17242 · Topic: CUET UG 2022 Applied Mathematics · Just now
CUET UG 2022 Applied Mathematics

The solution of the differential equation $xdy-ydx=0$ represent family of

Solution

$xdy-ydx=0$

Divide by $dx$:

$x\frac{dy}{dx}-y=0$

So,

$x\frac{dy}{dx}=y$

$\frac{dy}{dx}=\frac{y}{x}$

Separate variables:

$\frac{dy}{y}=\frac{dx}{x}$

Integrate:

$\log|y|=\log|x|+C$

$\log\left|\frac{y}{x}\right|=C$

$\frac{y}{x}=k$

$y=kx$

This represents straight lines passing through origin.
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