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(D) Given the differential equation: $\frac{dy}{dx} = \sec y$. Separating the variables,we get: $\cos y \, dy = dx$. Integrating both sides: $\int \co

Vedclass · Accepted Answer

$x = \sin y$

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(D) Given the differential equation: $\frac{dy}{dx} = \sec y$. Separating the variables,we get: $\cos y \, dy = dx$. Integrating both sides: $\int \cos y \, dy = \int dx$. This gives: $\sin y = x + c$. Using the initial condition $y(0) = 0$,we substitute $x = 0$ and $y = 0$: $\sin(0) = 0 + c$,which implies $c = 0$. Substituting $c = 0$ back into the general solution,we get: $\sin y = x$,or $x = \sin y$. Thus,the correct option is $D$.

The particular solution of the differential equation $\frac{dy}{dx} = \sec y$ with the initial condition $y(0) = 0$ is:

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