5. Write the following higher-order differential equations as equivalent systems of (first order) differential equations: (a) r" – 21" + 5x' + 10x = t³e# + 2x" + 5(x")3 +t*rr' + cos(x) = 1+ t2 Do NOT write these in matrix-vector form. (b) x"

5. Write the following higher-order differential equations as equivalent systems of (first order) differential equations: (a) r" – 21" + 5x' + 10x = t³e# + 2x" + 5(x")3 +t*rr' + cos(x) = 1+ t2 Do NOT write these in matrix-vector form. (b) 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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5. Write the following higher-order differential equations as equivalent systems of (first order)
differential equations:
(a) a" – 2a" + 5æ' + 10x = t°e2t
4
(b) a" + 2x" + 5(a")3 +t*xx' + cos(x) =
1+ t2
Do NOT write these in matrix-vector form.

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