Math 54 quiz 9 find a general solution to the differential

Question

MATH 54 QUIZ 9-

1. Find a general solution to the differential equation y'' + 8y' + 16y = 0.

2. Solve the initial value problem: {y'' + 2y' + y = 0, y(0) = 1, y'(0) = -3}.

3. Find a general solution to the differential equation y''' - y''+ 2y = 0.

4. Find a general solution to the differential equation y⁽⁴⁾ + 13y'' + 36y = 0.

5. True/False? Justify your answer. Let a(≠0), b, c, d be constants, and let y₁, y₂, y₃ be solutions to ay''' + by'' + cy' + dy = 0 on R. If W[y₁, y₂](x₀) = 0 for some x₀ ∈ R, then W[y₁, y₂, y₃](x₀) = 0.

6. Show that {1, ln t, e^t, sin t} is linearly independent on (0, ∞).