The discussion focuses on solving the differential equation D²x - 2x = 2sin(2t) with initial conditions x(0) = 0 and x'(0) = 1. The participant attempts to apply the Laplace transform, leading to the equation s²ƒ[x] - sx(0) - x'(0) - 2ƒ[x] = 2sin(2t). The solution process involves manipulating this equation to isolate ƒ[x], but the user encounters difficulties with arithmetic and parentheses, which are critical for accurate calculations. A suggestion is made to carefully check the arithmetic and the use of parentheses to avoid further errors.
PREREQUISITESStudents studying differential equations, particularly those learning to apply Laplace transforms, as well as educators looking for examples of common mistakes in solving such equations.
dumbengineer said:Homework Statement
D^2 x -2x = 2sin2t x(0) = 0 , x'(0) = 1
Homework Equations
D^2 x = s^2ƒ[x] - sx(0) - x'(o)
The Attempt at a Solution
s^2ƒ[x] - sx(0) - x'(o) - 2ƒ[x] = 2sin2t
s^2ƒ[x] - sx(0) - x'(o) - 2ƒ[x] = 4 / s^2 + 4
ƒ[x] (s^2 + 1) + 1 = 4 / s^2 +4