A third order linear, homogeneous DE whose general solution is is: y(t)= c1e^(t) + c2e^(2t) = c3e^(3t) [Hint: The general solution implies that r=1,2 and 3 are the roots of the characteristic equation of the DE. Hence r-1, r-2 and r-3 are the factors of the characteristic equation.] A. none of these B. y'''-6y''-11y'-6y=0 C. y'''+6y''-11y'-6y=0 D. y'''+6y''+11y'-6y=0 E. y'''-6y''+11y'-6y=
(a)A third order linear, homogeneous DE whose general solution is is: y(t)= c1e^(t) + c2e^(2t) = c3e^(3t)
[Hint: The general solution implies that r=1,2 and 3 are the roots of the characteristic equation of the DE. Hence r-1, r-2 and r-3 are the factors of the characteristic equation.]
A. none of these
B. y'''-6y''-11y'-6y=0
C. y'''+6y''-11y'-6y=0
D. y'''+6y''+11y'-6y=0
E. y'''-6y''+11y'-6y=
(b) Solving the DE; dx/dt = (t+x)/t, t>0
x(t) = Int^(t) +Ct
with the homogeneous method yields
where C is an arbitrary constant.
True or False?
(c)The general solution to the DE in the initial value problem (IVP)
y'''+8y'+16y = 0
y(0)= 1
y'(0)=4
.
y(x)=C1xe^(-4x) +Ce^(-4x)
Imposing the initial conditions, the values of the constants C1 and C2 are
C1=
C2=
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