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5. For the non-homogeneous differential equation x²y" – 4xy' + 6y =2x* + x² a) Show that x2, x3each satisfy the homogeneous differential equation. b) Show that x²,x³ are linearly independent

5. For the non-homogeneous differential equation x²y" – 4xy' + 6y =2x* + x² a) Show that x2, x3each satisfy the homogeneous differential equation. b) Show that x²,x³ are linearly independent

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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Answer 5b. For the non-homogeneous differential equation ?^2?′′ − 4??′ + 6? =2?^4 + ?^2
5. For the non-homogeneous differential equation x²y" – 4xy' + 6y =2x* + x? a) Show that x²,x³each satisfy the homogeneous differential equation. b) Show that x²,x³ are linearly independent c) Show that y, = x* – x² lnx over the interval (0,0) is the particular solution to the non-homogeneous differential equation d) Write the general solution to the non-homogeneous differential equation
Transcribed Image Text:5. For the non-homogeneous differential equation x²y" – 4xy' + 6y =2x* + x? a) Show that x²,x³each satisfy the homogeneous differential equation. b) Show that x²,x³ are linearly independent c) Show that y, = x* – x² lnx over the interval (0,0) is the particular solution to the non-homogeneous differential equation d) Write the general solution to the non-homogeneous differential equation
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