Find the solution to the initial value problem: x" + 25x = (µ+5)cos µt x(0) = 0 x'(0) = 0 1 1 x(t) = µ – 5 µ -5COS(ut) | x Write x(t) as a product of two sines, one with the beat (slow) frequency (µ – 5)/2 , and the other with the carrier (fast) frequency (µ+ 5)/2. x(t) = The solution x(t) is really a function of two variables t and u. Compute the limit of x(t,µ) as µ approaches 5 (your answer should be a function of t). lim x(t,u) = Define y(t) = lim x(t,u) Now let u approach 5 in the differential equation satisfied by x(t) to find a differential equation that y(t) satisfies. y" + y =

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.