x = e' + sin(x) ÿ=e* + cos(y) Xo =0 x₁ = 0 Yo =0 y = 0 (4.1) (4.2) (4.3) (4.4) (4.5) (4.6)
Consider the following second-order, nonlinear system of ordinary differential equations, and its initial conditions.
A. Linearize the right-hand sides of Eq. (4.1) and Eq. (4.2) about the stated initial conditions and simplify the resulting equations.
B. Transform the results in (A) to Laplace space using Laplace transforms and simplify. All X(s) terms and Y(s) terms should be on the left-hand side of both equations and all other terms should be on the right-hand side of both equations.
C. Solve for X(s) and Y(s).
D. Convert the right-hand-sides of the results in (C) to a form where the individual terms may be transformed back to time space using inverse Laplace transforms.
E. Apply inverse Laplace transforms to the result in (D).
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