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(D) Given the differential equation: $\cos^2 x \frac{d^2y}{dx^2} = 1$Step $1$: Rewrite the equation as $\frac{d^2y}{dx^2} = \sec^2 x$.Step $2$: Integr

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Both $(b)$ and $(c)$

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(D) Given the differential equation: $\cos^2 x \frac{d^2y}{dx^2} = 1$Step $1$: Rewrite the equation as $\frac{d^2y}{dx^2} = \sec^2 x$.Step $2$: Integrate both sides with respect to $x$ to find the first derivative:$\frac{dy}{dx} = \int \sec^2 x \, dx = 	an x + c_1$.Step $3$: Integrate again with respect to $x$ to find $y$:$y = \int (	an x + c_1) \, dx = \int 	an x \, dx + \int c_1 \, dx$.Since $\int 	an x \, dx = \log |\sec x|$,we get:$y = \log |\sec x| + c_1x + c_2$.Since $c_1$ is an arbitrary constant,it can be positive or negative. Thus,$y = \log \sec x \pm c_1x + c_2$ covers both options $(b)$ and $(c)$.

The solution of the differential equation $\cos^2 x \frac{d^2y}{dx^2} = 1$ is

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