Question

1. For which initial conditions will the solution of x"(t) + 2x'(t) - 8x(t) = 0 tend to zero as t ? ?? 2. Find the complete solution of x"(t) + 4x(t) = 5 cos(?t), x(0) = x'(0) = 0 when (a) ? ? 2 and (b) ? = 2 3. What can you say about the zeros of solutions of (a) x"(t) + \left(\frac{3+4t}{2+9t}\right)x(t) = 0 (b) x"(t) + \left(\frac{3-4t}{2+9t}\right)x(t) = 0 on [0, ?)? Explain. 4. Use the method of variation of parameters to find a particular solution of x"(t) - x(t) = f(t) = 1/(1 + t²) Leave the solutions in simplified integral form. 5. Find a solution to the system x' = 2x + y, y' = -6x + 7y with initial conditions x(0) = 2, y(0) = 1

          1. For which initial conditions will the solution of x"(t) + 2x'(t) - 8x(t) = 0 tend to zero as t ? ??
2. Find the complete solution of
x"(t) + 4x(t) = 5 cos(?t), x(0) = x'(0) = 0
when
(a) ? ? 2 and
(b) ? = 2
3. What can you say about the zeros of solutions of
(a) x"(t) + \left(\frac{3+4t}{2+9t}\right)x(t) = 0
(b) x"(t) + \left(\frac{3-4t}{2+9t}\right)x(t) = 0
on [0, ?)? Explain.
4. Use the method of variation of parameters to find a particular solution of
x"(t) - x(t) = f(t) = 1/(1 + t²)
Leave the solutions in simplified integral form.
5. Find a solution to the system
x' = 2x + y, y' = -6x + 7y
with initial conditions x(0) = 2, y(0) = 1

1. For which initial conditions will the solution of x"(t) + 2x'(t) - 8x(t) = 0 tend to zero as t ? ??
2. Find the complete solution of
x"(t) + 4x(t) = 5 cos(?t), x(0) = x'(0) = 0
when
(a) ? ? 2 and
(b) ? = 2
3. What can you say about the zeros of solutions of
(a) x"(t) + ((3+4t)/(2+9t))x(t) = 0
(b) x"(t) + ((3-4t)/(2+9t))x(t) = 0
on [0, ?)? Explain.
4. Use the method of variation of parameters to find a particular solution of
x"(t) - x(t) = f(t) = 1/(1 + t²)
Leave the solutions in simplified integral form.
5. Find a solution to the system
x' = 2x + y, y' = -6x + 7y
with initial conditions x(0) = 2, y(0) = 1

Added by Mariah P.

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