Variation of Parameters for System of 1st order ODE

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Kreyszig Advanced Engineering Mathematics shows the variation of parameter method for a system of first order ODE: $$\underline{y}' = \underline{A}(x)\underline{y} + \underline{g}(x)$$ The particular solution is: $$\underline{y}_p = \underline{Y}(x)\underline{u}(x)$$ where $\underline{Y}(x)$ is the homogeneous solution and: $$\underline{u}(x) = \int_0^x \underline{Y}^{-1}\underline{g}$$ But, for for a single 2nd order non-homogeneous ODE $y'' + p(x) y' + q(x) y = r(x)$ the solution is:$$y_p = y_1 \int \frac{y_2}{W}r(x)dx + y_2 \int \frac{y_1}{W}r(x)dx$$ where $y_1, \, y_2$ are the solutions to the homogeneous equation and $W$ is the Wronskian of the homogeneous solutions.

Why the definite integral in the case of systems but indefinite integral in the case of a single 2nd order ODE? The book offers no explanation.

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