Which of the following functions are solutions of the differential equation y′′−6y′+9y=0?
A. y(x)=x^2e^3x
B. y(x)=0
C. y(x)=xe^3x
D. y(x)=e^−3x
E. y(x)=3x
F. y(x)=3xe^−3x
G. y(x)=e^3x
yeah i suck at calc 2
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Verified answer
Find the general solution by solving the auxiliary equation:
y'' - 6y' + 9y = 0
m² - 6m + 9 = 0
(m - 3)² = 0
m - 3 = 0
m = 3
y = (C₁x + C₂)℮^(3x)
None of the functions given are solutions, as none of them are exponentials.