Question

Find constants a and b which make the function x(t)=acos(t)+bsin(t) a solution to the differential equation d^{2}x/dt^{2 }- dx/dt^{ }= cos(t)

Step 1

If x(t)=a cos (t) + b sin(t) is a solution to the differential equation d^{2}x/dt^{2 }- dx/dt^{ }= cos(t) then x(t) = a cos(t) + b sin(t) satisfied the given differential equation.

So, differentiate x(t) = a cos(t) + b sin(t) with respect to the variable (t).

Step 2

Again, differentiate with respect to t:

Step 3

Substitute the expression of dx/dt and d2x/dt2

In the equation d2x/dt2&...

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