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The equation $\dfrac{dy}{dx} = xy^{2}+ 2y+ x- 4.5$ with the initial condition $y(x= 0) = 1$ is to be solved using a predictor-corrector approach. Use a predictor based on the implicit Euler's method and a corrector based on the trapezoidal rule of integration, each with a full-step size of $0.5$. Considering only positive values of $y$, the value of $y$ at $x = 0.5$ is  _____________________ (rounded off to three decimal places).

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