wksht06sol - MATH 152 L1 & L2 Applied Linear...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 152 L1 & L2 Applied Linear Algebra and Differential Equations Spring 2004-05 ¥ Week 06 Worksheet Solutions : Laplace Transform Q1. (Initial value problem) Consider the initial value problem y- y = e 2 t , y (0) = 1. (a) Show that L{ y ( t ) } = s L{ y ( t ) } - y (0). Solution The formula follows from integration by parts, L{ y ( t ) } def. = Z ∞ e- st y ( t ) dt = Z ∞ e- st d ( y ( t )) = e- st y ( t ) fl fl fl t = ∞ t =0 + s Z ∞ e- st y ( t ) dt =- y (0) + s L{ y ( t ) } . (b) Apply the Laplace transform to both sides of the given equation, and then determine L{ y ( t ) } . Solution Applying the Laplace transform to the differential equation, we have L{ y- y } = L{ e 2 t } . By the linearity of L , we have L{ y } - L{ y } = L{ e 2 t } , [ s L{ y } - y (0)]- L{ y } = 1 s- 2 , ( s- 1) L{ y } = 1 s- 2 + 1 = s- 1 s- 2 , L{ y ( t ) } = 1 s- 2 . (c) Apply the inverse Laplace transform to find y ( t ) from L{ y ( t ) } ....
View Full Document

Page1 / 3

wksht06sol - MATH 152 L1 & L2 Applied Linear...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online