1) Answer without referring back to the text. Fill in the blank. (Enter your ans
ID: 3210127 • Letter: 1
Question
1) Answer without referring back to the text. Fill in the blank. (Enter your answers as a comma-separated list. Enter all answers using the appropriate multiplicities.)
If y = 3 x + x2 + 8ex
is a solution of a homogeneous fourth-order linear differential equation with constant coefficients, then the roots of the auxiliary equation are?
2) Use systematic elimination to solve the following system:
Any help in producing the correct answers would be greatly appreciated! Thanks in advance.
dx/dt = 2x + y + t 2 dy/dt = 3x + 4y 4tExplanation / Answer
1. y = 3 – x +x2 + 8ex
The equation is of the form
Y = (C1 + C2x + C3x2 )emx + C4 enx
Where, m is repeated root (thrice) and n is the fourth root
On comparing,
C1 = 3 , C2 = -1, C3 = 1 , C4 = 8, m = 0, n = 1
The roots are 0, 0, 0, 1
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