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Question

(B) Given the differential equation: $\frac{dy}{dx} + \frac{1 + x^2}{x} = 0$ Separate the variables: $dy = - \left( \frac{1 + x^2}{x} \right) dx$ Simp

Vedclass · Accepted Answer

$y + \log |x| + \frac{x^2}{2} + c = 0$

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(B) Given the differential equation: $\frac{dy}{dx} + \frac{1 + x^2}{x} = 0$ Separate the variables: $dy = - \left( \frac{1 + x^2}{x} \right) dx$ Simplify the expression: $dy = - \left( \frac{1}{x} + x \right) dx$ Integrate both sides: $\int dy = - \int \left( \frac{1}{x} + x \right) dx$ $y = - (\log |x| + \frac{x^2}{2}) + c$ $y = - \log |x| - \frac{x^2}{2} + c$ Rearranging the terms: $y + \log |x| + \frac{x^2}{2} = c$ Thus,the correct option is $B$.

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

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