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5. Consider the nonhomogeneous linear equation dy + 2y = 3t2 + 2t – 1. dt In order to find the general solution, we must guess a particular solution yp(t). Since the right-hand side is a quadratic polynomial, it is reasonable to guess a quadratic for y,(t), so let Yp(t) = at? + bt + c, where a, b, and c are constant. Determine values for these constants so that yp(t) is a solution.

5. Consider the nonhomogeneous linear equation dy + 2y = 3t2 + 2t – 1. dt In order to find the general solution, we must guess a particular solution yp(t). Since the right-hand side is a quadratic polynomial, it is reasonable to guess a quadratic for y,(t), so let Yp(t) = at? + bt + c, where a, b, and c are constant. Determine values for these constants so that yp(t) is a solution.

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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5. Consider the nonhomogeneous linear equation dy + 2y = 3t2 + 2t – 1. dt In order to find the general solution, we must guess a particular solution yp(t). Since the right-hand side is a quadratic polynomial, it is reasonable to guess a quadratic for y,(t), so let Yp(t) = at? + bt + c, where a, b, and c are constant. Determine values for these constants so that y,(t) is a solution.
Transcribed Image Text:5. Consider the nonhomogeneous linear equation dy + 2y = 3t2 + 2t – 1. dt In order to find the general solution, we must guess a particular solution yp(t). Since the right-hand side is a quadratic polynomial, it is reasonable to guess a quadratic for y,(t), so let Yp(t) = at? + bt + c, where a, b, and c are constant. Determine values for these constants so that y,(t) is a solution.
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