Question

If x1(t) and x2(t) are solutions to the differential equation

x"+bx'+cx = 0

1. Is x= x1+x2+c for a constant c always a solution?
(I think No, except for the case of c=0)

2. Is tx1 a solution? (t is a constant)

I have to show all works of the whole process, please help me!

Answer #1

1. If x1(t) and x2(t) are solutions to the differential
equation
x" + bx' + cx = 0
is x = x1 + x2 + c for a constant c always a solution? Is the
function y= t(x1) a solution?
Show the works
2. Write sown a homogeneous second-order linear differential
equation where the system displays a decaying oscillation.

dX(t) = bX(t)dt + cX(t)dW(t) for contant values of X(0), b and
c
(a) Find E[X(t)] (hint: look at e ^(−bt)X(t))
(b) The Variance of X(t)

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