Find the general solution of the given differential equation using variation of parameters.

Question

y‴ + 100y′ = sec10t, −π / 20 < t < π / 20

Choices:

1. y = c₁+c₂cos10t + c₃sin10t + 0.001 ln |sec10t + tan10t| − 0.01t + 0.001 ln (cos10t)
2. y = c₁ + c₂cos10t + c₃sin10t + 0.001 ln |sec10t + tan10t| − 0.01tcos10t + 0.001 sin10t ln(cos10t)
3. y = 1 + cos10t + sin10t + c₁ ln|sec10t+tan10t|− c₂tcos10t + c₃sin10t ln(cos10t)
4. y = c₁ + c₂cos10t + c₃sin10t + c₄ln|sec10t+tan10t| − c₅tcos10t + c₆sin10t ln(cos10t)

Answer 1

Option B is the correct answer. Unfortunately, I can't write it out because it's a lengthy problem and exceeds the word count on Wyzant.