This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able tocome back to the skipped part.Consider the following differential equation.4y" + 2y'- 2y 0Exercise (a)For what values of r does the function y = ex satisfy the equation?Click here to begin!Exercise (b)If ri and r, are the values of r that you found in part (a), show that every member of the family of functionsy = ae'1x + be'2x is also a solution.Step 1We must decide whether 4f "(x) + 2f'(x) - 2f(x) = 0 for f(x) = aex/2 + be-X.We have f'(x) =and f"(x) =Submit Skip (you cannot come back)

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Consider the following differential equation. 4y" + 2y' - 2y = 0 Exercise (a) For what values of r does the functlon y - ex satisfy the equation? Click here to begin! Exercise (b) If r, and r are the values of r that you found in part (a), show that every member of the family of functions y = ae'ix + be'2x is also a solution. Step 1 We must decide whether 4f"(x) + 2f'(x) - 2f(x) - 0 for f(x) = ae/2 + be-x. We have f'(x) = and f"(x) =

Consider the following differential equation. 4y" + 2y' - 2y = 0 Exercise (a) For what values of r does the functlon y - ex satisfy the equation? Click here to begin! Exercise (b) If r, and r are the values of r that you found in part (a), show that every member of the family of functions y = ae'ix + be'2x is also a solution. Step 1 We must decide whether 4f"(x) + 2f'(x) - 2f(x) - 0 for f(x) = ae/2 + be-x. We have f'(x) = and f"(x) =

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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