The solution of the differential equation x s | vedclass

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(B) Given the differential equation: $x \sec y \frac{dy}{dx} = 1$ Separate the variables: $\sec y \, dy = \frac{1}{x} \, dx$ Integrate both sides: $\i

Vedclass · Accepted Answer

$cx = \sec y + 	an y$

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(B) Given the differential equation: $x \sec y \frac{dy}{dx} = 1$ Separate the variables: $\sec y \, dy = \frac{1}{x} \, dx$ Integrate both sides: $\int \sec y \, dy = \int \frac{1}{x} \, dx$ We know that $\int \sec y \, dy = \log |\sec y + 	an y|$ and $\int \frac{1}{x} \, dx = \log |x| + \log |c|$ So,$\log |\sec y + 	an y| = \log |cx|$ Taking the exponential on both sides,we get: $\sec y + 	an y = cx$

The solution of the differential equation $x \sec y \frac{dy}{dx} = 1$ is

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