Consider the differential equation Lu = f, with the differential equation in the attached image. with ai(t) sufficiently smooth and a2(t) ≠ 0 for all t. Suppose u0 is a solution of the homogeneous equation Lu = 0, with u0(t) ≠ 0 for all t. We are going to apply Lagrange's "variation of constant" to the general solution to find. Suppose the solution u is of the form u = u0v a. From the equation Lu = f, derive a second order equation for v, in terms of u0 , u0' and f. b. Call w = v' and solve the obtained differential equation for w. c. Calculate the solution u.
Consider the differential equation Lu = f, with the differential equation in the attached image. with ai(t) sufficiently smooth and a2(t) ≠ 0 for all t. Suppose u0 is a solution of the homogeneous equation Lu = 0, with u0(t) ≠ 0 for all t. We are going to apply Lagrange's "variation of constant" to the general solution to find. Suppose the solution u is of the form u = u0v a. From the equation Lu = f, derive a second order equation for v, in terms of u0 , u0' and f. b. Call w = v' and solve the obtained differential equation for w. c. Calculate the solution u.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Consider the
with ai(t) sufficiently smooth and a2(t) ≠ 0 for all t.
Suppose u0 is a solution of the homogeneous equation Lu = 0, with u0(t) ≠ 0 for
all t. We are going to apply Lagrange's "variation of constant" to the general solution
to find. Suppose the solution u is of the form u = u0v
a. From the equation Lu = f, derive a second order equation for v, in terms of
u0 , u0' and f.
b. Call w = v' and solve the obtained differential equation for w.
c. Calculate the solution u.
Transcribed Image Text:n (7)⁰p +
dt
du
+ a₁ (t)
z7P
n z p
a₂
(7) ²D = n T
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