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Question

(A) Given the differential equation: $\frac{dx}{x} + \frac{dy}{y} = 0$. Integrating both sides,we get: $\int \frac{dx}{x} + \int \frac{dy}{y} = \int 0

Vedclass · Accepted Answer

$xy = c$

Vedclass · Answer

(A) Given the differential equation: $\frac{dx}{x} + \frac{dy}{y} = 0$. Integrating both sides,we get: $\int \frac{dx}{x} + \int \frac{dy}{y} = \int 0$. This results in: $\log |x| + \log |y| = C_1$. Using the logarithmic property $\log a + \log b = \log(ab)$,we have: $\log |xy| = C_1$. Taking the exponential of both sides,we get $|xy| = e^{C_1}$. Letting $e^{C_1} = c$,we obtain the final solution: $xy = c$.

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

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