We have a differential equation y + p(x)y' +q(x)y = F(x) with general solution y =...
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We have a differential equation y" + p(x)y' +q(x)y = F(x) with general solution y = y₁ + y2 + Yp Ур y₁ and y2 are linearly independent solutions to the homogeneous equation and a particular solution to the inhomogeneous equation. Assume here that Y1 and Y2₂ include the arbitrary constants. Show that one form for Yp is given by Y₁(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) = y₁92 - ₁92. is We have a differential equation y" + p(x)y' +q(x)y = F(x) with general solution y = y₁ + y2 + Yp Ур y₁ and y2 are linearly independent solutions to the homogeneous equation and a particular solution to the inhomogeneous equation. Assume here that Y1 and Y2₂ include the arbitrary constants. Show that one form for Yp is given by Y₁(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) = y₁92 - ₁92. is
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Given differential equation is ypxyqxyFx 0 the complementary solution to i is ... View the full answer
Related Book For
A First Course in Differential Equations with Modeling Applications
ISBN: 978-1111827052
10th edition
Authors: Dennis G. Zill
Posted Date:
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