2. a. b. Find the general solution to the fifth order differential equation given in operator notation as or 2 d² d (4-4) (-44 +¹³)* -0 13 dx dx² dx (D− 4) (D² − 4D+13) ²y = 0, d dx Find a linear homogeneous constant-coefficient differential equation with general solution given by where D = y(x)=A+Bx+Ce-2x cos(3x) + De-2x sin(3x) + (E+Fx)e¯*. Show all work. You can leave your answer for the differential equation in a factored form like part (a), but the coefficients must be real numbers.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
2.
a.
b.
Find the general solution to the fifth order differential equation given in operator
notation as
or
2
d
d
(4-4) (42²2-44 +13) ² y =
0
dx
dx² dx
(D − 4) (D² − 4D +13)² y:
y = 0,
d
dx
Find a linear homogeneous constant-coefficient differential equation with general
solution given by
y(x) = A + Bx+Ce-2x cos(3x) + De-2x sin(3x) + (E+Fx)e¯*.
where D =
Show all work. You can leave your answer for the differential equation in a factored form
like part (a), but the coefficients must be real numbers.
Transcribed Image Text:2. a. b. Find the general solution to the fifth order differential equation given in operator notation as or 2 d d (4-4) (42²2-44 +13) ² y = 0 dx dx² dx (D − 4) (D² − 4D +13)² y: y = 0, d dx Find a linear homogeneous constant-coefficient differential equation with general solution given by y(x) = A + Bx+Ce-2x cos(3x) + De-2x sin(3x) + (E+Fx)e¯*. where D = Show all work. You can leave your answer for the differential equation in a factored form like part (a), but the coefficients must be real numbers.
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