Questions
MTH1030 -1035 - S1 2025 MTH1030/35 Week 11 lesson quiz: Differential equations
Single choice
Which of the following is a solution of the differential equation \(y''+y=0\)?
Options
A.a. \(\sin(x)+5 \cos(x)\)
B.b. \(\sin(x)+5 \cos(2x)\)
C.c. \(6e^{3x}-4xe^{3x}\)
D.d. \(4e^{-3x}\)
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Step-by-Step Analysis
Consider the differential equation y'' + y = 0, whose general solutions are linear combinations of cos x and sin x, i.e., y = A cos x + B sin x.
Option a: y = sin(x) + 5 cos(x). Compute derivatives: y' = cos(x) - 5 sin(x), y'' = -sin(x) - 5 cos(x). Then y'' + y = (-sin(......Login to view full explanationLog in for full answers
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Consider the differential equation: . If the general solution is , which one of the following is the value of ?
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