y" -y - 2y = 0.Assume that y, (t) = e and y, (t) = et form a fundamental set of solutions.(b) LetY3 (1) = -4e24 (t) = y1 (t) +4y2 (?)ys (t) = 4y, (t) – 4 y3 (t).Are y3 (t), y4 (t), and ys (t) also solutions of the given differential equation?O YesO NoO Impossible to tell (c) Determine which of the following pairs forms a fundamental set of solutions:[v(), y3 (?)] : [»> ( ), v3 (): > (), va (0)]; [v. (e), v().O (), y3 ()] - b» (), ya (1) , and [va (e), ys (t)]O y. (t), ys (1)] and [y2 (t). ys (1)]O y2 (), y ()] and [yi (1), y4()] and fy, (t). ys (1)]• ly (?), ya (*)] and [vı (t). va (2)]O y (1), y ()]) [>() ys (1)] , and [y, (t), ys (t)]Click if you would like to Show Work for this question: Open Show Work

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Assume that y, (1) = e and y, (1) = e" form a fundamental set of solutions. (b) Let y3 (t) = -4e2 Ya (t) = y1 () + 4y () ys (t) = 4y, (t) – 4 y, (). Are y, (t), y4 (1), and ys (t) also solutions of the given differential equation? O Yes O No O Impossible to tell

Assume that y, (1) = e and y, (1) = e" form a fundamental set of solutions. (b) Let y3 (t) = -4e2 Ya (t) = y1 () + 4y () ys (t) = 4y, (t) – 4 y, (). Are y, (t), y4 (1), and ys (t) also solutions of the given differential equation? O Yes O No O Impossible to tell

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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y" -y - 2y = 0.
Assume that y, (t) = e and y, (t) = et form a fundamental set of solutions.
(b) Let
Y3 (1) = -4e2
4 (t) = y1 (t) +4y2 (?)
ys (t) = 4y, (t) – 4 y3 (t).
Are y3 (t), y4 (t), and ys (t) also solutions of the given differential equation?
O Yes
O No
O Impossible to tell

(c) Determine which of the following pairs forms a fundamental set of solutions:
[v(), y3 (?)] : [»> ( ), v3 (): > (), va (0)]; [v. (e), v().
O (), y3 ()] - b» (), ya (1) , and [va (e), ys (t)]
O y. (t), ys (1)] and [y2 (t). ys (1)]
O y2 (), y ()] and [yi (1), y4()] and fy, (t). ys (1)]
• ly (?), ya (*)] and [vı (t). va (2)]
O y (1), y ()]) [>() ys (1)] , and [y, (t), ys (t)]
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