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Introduction to Linear Algebra

Exercise 3.4.40

Answers

(a): The functions $y = \sin x, y = \cos x, y = e^{x}, y = e^{- x}$ are a basis for solutions to $d^{4} y ∕ d x^{4} = y (x)$ .
(b): A particular solution to $d^{4} y ∕ d x^{4} = y (x) + 1$ is $y (x) = - 1$ . The complete solution is $y (x) = - 1 + c_{1} \sin x + c_{2} \cos x + c_{3} e^{x} + c_{4} e^{- x}$ (or use another basis for the nullspace of the 4 th derivative).

mathchakra

2022-01-23 16:00

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