Ononot — For the Riccati equation \frac{dy}{dx} = 1 + x^2 - y^2, it i

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Differential Equationshard

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For the Riccati equation $\frac{dy}{dx} = 1 + x^2 - y^2$ , it is observed that $y_1(x) = x$ is a particular solution. If we substitute $y = x + \frac{1}{v}$ , what linear differential equation does $v(x)$ satisfy?