For a third-order homogeneous differential equation the general solution is given by Yg (t) = c1f (t) + c2g (t) + c3h (t). Which of the following statement (s) is/are correct? f (t) I : +h (t) may be a constant g(t) II : The functions f,g, and h may have maximum at same point to III : Wronskian of the functions f, g, and h is nonzero A) I and III В) II and III C) only III D) only II E)I and II

For a third-order homogeneous differential equation the general solution is given by Yg (t) = c1f (t) + c2g (t) + c3h (t). Which of the following statement (s) is/are correct? f (t) I : +h (t) may be a constant g(t) II : The functions f,g, and h may have maximum at same point to III : Wronskian of the functions f, g, and h is nonzero A) I and III В) II and III C) only III D) only II E)I and II

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

For a third-order homogeneous differential equation the general solution is given by
Yg (t) = c1f (t) + c2g (t) + c3h (t).
Which of the following statement (s) is/are correct?
f (t)
I :
+h (t) may be a constant
g(t)
II : The functions f,g, and h may have maximum at same point to
III : Wronskian of the functions f, g, and h is nonzero
A) I and III
B) II and III
C) only III
D) only II
E)I and II

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