One process can be modeled using the following differential equation: y′(t)=3(u(t)−y(t)), y(0)=0.Calculate the solution of the differential equation knowing that u(t) isTutorial: Draw a defined u and represent u as the sum of the Heaviside step functions. Solve the differential equation with the Laplace transform.Answer: y is defined by pieces Erästä prosessia voidaan mallintaa seuraavan differentiaaliyhtälön avullay' (t) = 3(u(t) – y(t)), y(0) = 0.Laske differentiaaliyhtälön ratkaisu kun tiedetään, että u(t) onu(t) = {;1, 0 2.Opastus: Piirrä paloittain määritelty u ja esitä u Heavisiden askelfunktioiden summana. Ratkaisedifferentiaaliyhtälö Laplace-muunnoksella.Vastaus: y paloittain määriteltynä ony(t)0 2.

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Answered: Erästä prosessia voidaan mallintaa…

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Erästä prosessia voidaan mallintaa seuraavan differentiaaliyhtälön avulla y' (t) = 3(u(t) – y(t)), y(0) = 0. -

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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Question

One process can be modeled using the following differential equation: y′(t)=3(u(t)−y(t)), y(0)=0.

Calculate the solution of the differential equation knowing that u(t) is

Tutorial: Draw a defined u and represent u as the sum of the Heaviside step functions. Solve the differential equation with the Laplace transform.

Answer: y is defined by pieces

Erästä prosessia voidaan mallintaa seuraavan differentiaaliyhtälön avulla
y' (t) = 3(u(t) – y(t)), y(0) = 0.
Laske differentiaaliyhtälön ratkaisu kun tiedetään, että u(t) on
u(t) = {;
1, 0<t< 2,
5, t> 2.
Opastus: Piirrä paloittain määritelty u ja esitä u Heavisiden askelfunktioiden summana. Ratkaise
differentiaaliyhtälö Laplace-muunnoksella.
Vastaus: y paloittain määriteltynä on
y(t)
0<t< 2
y(t)
,t> 2.

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