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Question

(B) Given differential equation is $y \ dx - x \ dy = xy \ dx$. Dividing both sides by $xy$,we get: $\frac{y \ dx - x \ dy}{xy} = dx$ This can be writ

Vedclass · Accepted Answer

$x = y e^x$

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(B) Given differential equation is $y \ dx - x \ dy = xy \ dx$. Dividing both sides by $xy$,we get: $\frac{y \ dx - x \ dy}{xy} = dx$ This can be written as: $d \left( \log \left( \frac{x}{y} \right) \right) = dx$ Integrating both sides: $\int d \left( \log \left( \frac{x}{y} \right) \right) = \int dx$ $\log \left( \frac{x}{y} \right) = x + C$ Assuming the constant of integration $C = 0$ for the given options: $\log \left( \frac{x}{y} \right) = x$ $\frac{x}{y} = e^x$ $x = y e^x$

The solution of the differential equation $y \ dx - x \ dy = xy \ dx$ is . . . . . .

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