Question
We have a differential equation y + p(x)y' +q(x)y = F(x) with general solution y = y + y2 + Yp y and y2
We have a differential equation y" + p(x)y' +q(x)y = F(x) with general solution y = y + y2 + Yp y and y2 are linearly independent solutions to the homogeneous equation and a particular solution to the inhomogeneous equation. Assume here that Y1 and Y2 include the arbitrary constants. Show that one form for Yp is given by Y(x) F(x) dx W(x) Yp = y2 S where W(x) is the Wronskian: Y1 dx [ 192 (x) F(x) dr. I W(x) = y92 - 92. is
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A First Course in Differential Equations with Modeling Applications
Authors: Dennis G. Zill
10th edition
978-1111827052
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