AP Calculus AB 7.2 Verifying Solutions for Differential Equations - MCQs - Exam Style Questions
No-Calc Question
The equation \(y=2e^{6x}-5\) is a particular solution to which of the following differential equations?
(A) \(y’-6y-30=0\)
(B) \(2y’-12y+5=0\)
(C) \(y”-5y’-6y=0\)
(D) \(y”-2y’+y+5=0\)
(B) \(2y’-12y+5=0\)
(C) \(y”-5y’-6y=0\)
(D) \(y”-2y’+y+5=0\)
▶️ Answer/Explanation
Compute \(y’ = 12e^{6x}\).
Substitute in (A): \(y’-6y-30 = 12e^{6x}-6(2e^{6x}-5)-30 = 0\).
(B),(C),(D) do not simplify to \(0\) for all \(x\).
✅ Answer: (A)
Substitute in (A): \(y’-6y-30 = 12e^{6x}-6(2e^{6x}-5)-30 = 0\).
(B),(C),(D) do not simplify to \(0\) for all \(x\).
✅ Answer: (A)