I know the exercise is in Spanish, but it is easy to understand. 2xDemuestre que y=cje* + cze* +cze +3 es una solución de y!ll -2y || - y + 2y = 6 (justificar).

Answered: 2x Demuestre que y=c1ex + c2e* + c z e…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

I know the exercise is in Spanish, but it is easy to understand.

2x
Demuestre que y=cje* + cze* +cze +3 es una solución de y!ll -2y || - y + 2y = 6 (justificar).

Expert Solution

Step 1

Here, we need to justify that $y = c_{1} e^{x} + c_{2} e^{- x} + c_{3} e^{2 x} + 3$ is the solution of $y''' - 2 y'' - y' + 2 y = 6$ .

Now,

$y' = (c_{1} e^{x} + c_{2} e^{- x} + c_{3} e^{2 x} + 3)' = c_{1} e^{x} + 2 c_{3} e^{2 x} - c_{2} e^{- x} y'' = (c_{1} e^{x} + c_{2} e^{- x} + c_{3} e^{2 x} + 3)'' = (c_{1} e^{x} + 2 c_{3} e^{2 x} - c_{2} e^{- x})' = c_{1} e^{x} + 4 c_{3} e^{2 x} + c_{2} e^{- x} y''' = (c_{1} e^{x} + c_{2} e^{- x} + c_{3} e^{2 x} + 3)''' = (c_{1} e^{x} + 2 c_{3} e^{2 x} - c_{2} e^{- x})'' = (c_{1} e^{x} + 2 c_{3} e^{2 x} - c_{2} e^{- x})' = c_{1} e^{x} + 8 c_{3} e^{2 x} - c_{2} e^{- x}$