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To solve the given initial value problem using the third-order Taylor series method, we begin with the general formula for Taylor series: $$ y_{n+1} = y_n + h y'_n + \frac{h^2}{2!} y''_n + \frac{h^3}{3!} y'''_n $$ where $y' = f(x, y)$, $y'' = \frac{d}{dx} f(x, y)$, and $y''' = \frac{d^2}{dx^2} f(x, y)$. Given $h = 0.1$ and the ______ ________ ______ _______ ________ ___ _______ ________ ________ _____ _______ ________.
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