With yp = 1 and yc = c1 cos x + c2 sin x in the notation of Problem, find a solution of y″ + y = 1 satisfying the initial conditions y(0) = −1 = y′(0).
Problem
Let yp be a particular solution of the nonhomogeneous equation y″ + py′ + qy = f(x) and let yc be a solution of its associated homogeneous equation. Show that y = yc + yp is a solution of the given nonhomogeneous equation.
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