The general solution of the differential equa | vedclass

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Question

(C) Given the differential equation: $\frac{x dy - y dx}{y} = 0$. Multiplying by $y$ (assuming $y 
eq 0$),we get: $x dy - y dx = 0$. Rearranging the

Vedclass · Accepted Answer

$y = c x$

Vedclass · Answer

(C) Given the differential equation: $\frac{x dy - y dx}{y} = 0$. Multiplying by $y$ (assuming $y 
eq 0$),we get: $x dy - y dx = 0$. Rearranging the terms: $x dy = y dx$. Separating the variables: $\frac{dy}{y} = \frac{dx}{x}$. Integrating both sides: $\int \frac{dy}{y} = \int \frac{dx}{x}$. This gives: $\ln|y| = \ln|x| + \ln|c|$. Using logarithmic properties: $\ln|y| = \ln|cx|$. Taking the exponential of both sides: $y = cx$.

The general solution of the differential equation $\frac{x dy - y dx}{y} = 0$ is . . . . . . .

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