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2. Solve dy dt =-y+28(t-3), y(0) = 1.

2. Solve dy dt =-y+28(t-3), y(0) = 1.

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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Question
Solve q 2 please
Note: Recall that the delta function 8(t) is the first derivative of the step function H(t). The key property of 8(t) is the way it behaves in integrals: for any number c and any function f, S.. [f(c), a<c<b, f(s)8(sc) ds = 0, otherwise, i.e. the integral "picks out" the value of the function f at the location c where 8(t-c) has a spike. The integral is zero if the spike lies outside the domain of integration. For integrals from 0 to t, when c> 0, we can rewrite the rule more concisely with a step function: 1. Evaluate the following integrals involving (t): [.. es cos(s) (s-2) ds. (a) (b) S [ f(s)8(s — c) ds = f(c)H(t - c). 2. Solve (8³+ s)8(s-2) ds. (c) S s² ln(1 + s)8(s 1) ds. (Your answer will depend on t.) =-y+28(t-3), y(0) = 1. dy dt
Transcribed Image Text:Note: Recall that the delta function 8(t) is the first derivative of the step function H(t). The key property of 8(t) is the way it behaves in integrals: for any number c and any function f, S.. [f(c), a<c<b, f(s)8(sc) ds = 0, otherwise, i.e. the integral "picks out" the value of the function f at the location c where 8(t-c) has a spike. The integral is zero if the spike lies outside the domain of integration. For integrals from 0 to t, when c> 0, we can rewrite the rule more concisely with a step function: 1. Evaluate the following integrals involving (t): [.. es cos(s) (s-2) ds. (a) (b) S [ f(s)8(s — c) ds = f(c)H(t - c). 2. Solve (8³+ s)8(s-2) ds. (c) S s² ln(1 + s)8(s 1) ds. (Your answer will depend on t.) =-y+28(t-3), y(0) = 1. dy dt
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