Consider a nonhomogeneous differential equation y" + 4y = -12x + 10e-*. (a) Verify that yp = -3x + 2e-* is a particular solution of the differential equation. (b) Show that 3x + 2e* is the Ye = c1 cos 2x + c2 sin 2x- general solution of the differential equation.

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A: The first order derivative of the function will take us to the result.

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A: Here we have f''θ=sinθ+cosθ, f(0)=5, f'(0) = 4 fθ=?

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A: The answer is in below step.

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A: Solving antiderivativ

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A: Topic = Differential equation

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A: Explanation of the answer is as follows

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A: Given

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A: Let's find.

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A: C'(x) = -425x +56∫C'(x) =∫ -425x +56C(x) = -425 x 2x2 +56x +kThe cost of producing 180 units…

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