In this problem you will solve the non-homogeneous differential equation y +12y + 32y = sin(e)...

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In this problem you will solve the non-homogeneous differential equation y" +12y + 32y = sin(e) (1) Let C₁ and C₂ be arbitrary constants. The general solution to the related homogeneous differential equation y" +12y' + 32y = 0 is the function y(x) = C₁ y₁(x) + C₂ y₂(x) = C₁ +C₂ NOTE: The order in which you enter the answers is important; that is, C₁f(x) + C₂g(x) # C₁9(x) + C₂f(x). (2) The particular solution y(a) to the differential equation y" +12y + 32y = sin(e) is of the form y₂(x) = y₁(x) u₁(x) + y₂(x) u₂(x) where u(x) = thus yp(x) = (4) The most general solution to the non-homogeneous differential equation y" +12y + 32y = sin(4x) y = C₁+₂+ (3) It follows that u₁(x) = and u₂(x)= A and u₂(x)= is In this problem you will solve the non-homogeneous differential equation y" +12y + 32y = sin(e) (1) Let C₁ and C₂ be arbitrary constants. The general solution to the related homogeneous differential equation y" +12y' + 32y = 0 is the function y(x) = C₁ y₁(x) + C₂ y₂(x) = C₁ +C₂ NOTE: The order in which you enter the answers is important; that is, C₁f(x) + C₂g(x) # C₁9(x) + C₂f(x). (2) The particular solution y(a) to the differential equation y" +12y + 32y = sin(e) is of the form y₂(x) = y₁(x) u₁(x) + y₂(x) u₂(x) where u(x) = thus yp(x) = (4) The most general solution to the non-homogeneous differential equation y" +12y + 32y = sin(4x) y = C₁+₂+ (3) It follows that u₁(x) = and u₂(x)= A and u₂(x)= is