Question: A differential equation is an equation involving an unknown function and its derivatives. Consider the differential equation y(t) + y(t) = 0. a. Show that

A differential equation is an equation involving an unknown function and its derivatives. Consider the differential equation y"(t) + y(t) = 0.

a. Show that y = A sin t satisfies the equation for any constant A.

b. Show that y = B cos t satisfies the equation for any constant B.

c. Show that y = A sin t + B cos t satisfies the equation for any constants A and B.

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