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.
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

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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