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(D) Given differential equation is $(x^2 + 1) \frac{dy}{dx} + (y^2 + 1) = 0$. Rearranging the terms to separate the variables,we get: $(x^2 + 1) \frac

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$(D) \ 	an^{-1} x + 	an^{-1} y = c$

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(D) Given differential equation is $(x^2 + 1) \frac{dy}{dx} + (y^2 + 1) = 0$. Rearranging the terms to separate the variables,we get: $(x^2 + 1) \frac{dy}{dx} = -(y^2 + 1)$ $\frac{dy}{y^2 + 1} = -\frac{dx}{x^2 + 1}$ Integrating both sides: $\int \frac{dy}{y^2 + 1} = -\int \frac{dx}{x^2 + 1}$ We know that $\int \frac{du}{u^2 + 1} = 	an^{-1} u + C$. Therefore,$	an^{-1} y = -	an^{-1} x + C$ $	an^{-1} x + 	an^{-1} y = C$.

The solution of the differential equation $(x^2 + 1) \frac{dy}{dx} + (y^2 + 1) = 0$ is . . . . . .

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