Question

Consider the following initial-value problem. dy/dt - y = 1, y(0) = 0 Find L{f(t)} for f(t) = 1. (Write your answer as a function of s.) L(f(t)) = 1/s Use the Laplace transform to solve the given initial-value problem. y(t) = e^t - 1

          Consider the following initial-value problem.

dy/dt - y = 1, y(0) = 0

Find L{f(t)} for f(t) = 1. (Write your answer as a function of s.)

L(f(t)) = 1/s

Use the Laplace transform to solve the given initial-value problem.

y(t) = e^t - 1

Consider the following initial-value problem.

dy/dt - y = 1, y(0) = 0

Find Lf(t) for f(t) = 1. (Write your answer as a function of s.)

L(f(t)) = 1/s

Use the Laplace transform to solve the given initial-value problem.

y(t) = e^t - 1

Added by Lori B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/06/2023

Step 1

First, we need to take the Laplace transform of the differential equation: ℒ{dy/dt - y = 1} = sY(s) - y(0) - Y(s) = 1/s Simplifying this expression, we get: sY(s) - Y(s) = 1/s Y(s) (s - 1) = 1/s Y(s) = 1/(s(s-1)) Now, we need to take the inverse Laplace Show more…

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Consider the following initial-value problem: dy/dt - y = 1, y(0) = 0. Find L{f(t)} for f(t) = 1. (Write your answer as a function of s.) L(f(t)) = ?. y(t) = ?