Find the general and particular solution of following linear ODE IVP & do detailed Curve Sketching analysis (Domain, Intercepts, Symmetry, Asymptotes, Intervals of Increase or Decrease, Local maximum and minimum, Concavity and points of Inflection, Sketch the function/ Plot the graph) of it (Particular solution). a. y' + 2y = 4 cos 2x, y(; 1) = 2 b. y' + 2y sin 2x = 2ecos 2x, y(0) = 0

Find the general and particular solution of following linear ODE IVP & do detailed Curve Sketching analysis (Domain, Intercepts, Symmetry, Asymptotes, Intervals of Increase or Decrease, Local maximum and minimum, Concavity and points of Inflection, Sketch the function/ Plot the graph) of it (Particular solution). a. y' + 2y = 4 cos 2x, y(; 1) = 2 b. y' + 2y sin 2x = 2ecos 2x, y(0) = 0

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.

Question

Find the general and particular
solution of following linear ODE IVP &
do detailed Curve Sketching analysis
(Domain, Intercepts, Symmetry,
Asymptotes, Intervals of Increase or
Decrease, Local maximum and
minimum, Concavity and points of
Inflection, Sketch the function/ Plot
the graph) of it (Particular solution).
a. y' + 2y = 4 cos 2x, y(; 1) = 2
b. y' + 2y sin 2x
= 2ecos 2x, y(0) = 0

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Solution:

Further follows,

Observation:

Conclusion:

Solution (b):

Further follows,

Observation:

Conclusion:

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