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Derivatives of Trigonometric Functions : Chain Rule

Use chain rule to verify that every function of the form

y = a sin (5t) + b cos (5t)

is a solution to the differential equation

d^2y/dt^2 = -25y.

Then use this fact to find the solution which also satisfies the initial conditions:

y(0) = 3 and y'(0) = 0

(^ means exponent and d^2y is over dt^2)

Solution Summary

The chain rule is applied to finding a derivative. The solution is detailed and well presented.