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This problem is about the constant coefficient linear inhomogeneous equation p(d/dx)y = f(x) where p(r) = (r + 1)(r− 2)². In the ta below, at left are various right sides f(z), and across from that at right is a form of a particular solution yp. For each line determine the constants from a, b, c such that yp, is a solution, or state that the given form is not a solution for any such values. A f = x², Yp = az² Yp = ax² + bx, Bƒ=1², c_f=1², Yp = az² + bx + c

This problem is about the constant coefficient linear inhomogeneous equation p(d/dx)y = f(x) where p(r) = (r + 1)(r− 2)². In the ta below, at left are various right sides f(z), and across from that at right is a form of a particular solution yp. For each line determine the constants from a, b, c such that yp, is a solution, or state that the given form is not a solution for any such values. A f = x², Yp = az² Yp = ax² + bx, Bƒ=1², c_f=1², Yp = az² + bx + c

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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This problem is about the constant coefficient linear inhomogeneous equation p(d/dx)y = f(x) where p(r) = (r + 1)(r− 2)². In the table below, at left are various right sides f(x), and across from that at right is a form of a particular solution yp. For each line determine the constants from a, b, c such that y, is a solution, or state that the given form is not a solution for any such values. A f = x², Yp = ax² B f = x², Ур = ax² + bx, c f = x², f = x²+3x+1, Yp = ax² + bx + c D Yp = ax² + bx + c, E f = e¹, 4x Yp = ae F f = e³, Yp = ae Gf=e³, H_f = e², | f = e², J f = e² Ур = axe 2x ae²z Yp = ae Yp = axe² Ур = az²e²x
Transcribed Image Text:This problem is about the constant coefficient linear inhomogeneous equation p(d/dx)y = f(x) where p(r) = (r + 1)(r− 2)². In the table below, at left are various right sides f(x), and across from that at right is a form of a particular solution yp. For each line determine the constants from a, b, c such that y, is a solution, or state that the given form is not a solution for any such values. A f = x², Yp = ax² B f = x², Ур = ax² + bx, c f = x², f = x²+3x+1, Yp = ax² + bx + c D Yp = ax² + bx + c, E f = e¹, 4x Yp = ae F f = e³, Yp = ae Gf=e³, H_f = e², | f = e², J f = e² Ур = axe 2x ae²z Yp = ae Yp = axe² Ур = az²e²x
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