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You have been given the following equation. It is a non-homogeneous differential equation. y" + 81y = sec²(9x) Assuming that c1 and c2 are arbitrary constants. The general solution to the related homogeneous differential equation of: y"+81y=0 is the function: yh(x) = C1y1(x) + C2y2(x) = C1_ Assuming yp(x) is the particular solution to the differential equation: y" + 81y = sec²(9x). yp(x) is of the form yp(x) = y1(x)u1(x) + y2(x)u2(x) where; u'1(x) = & u2(x) = It follows that u1(x) = And thus yp(x) = Knowing this, the most generalized solution to the non-homogeneous differential equation y" + 81y = sec (9x) Would be: y = C1 & u2(x) = + C2

You have been given the following equation. It is a non-homogeneous differential equation. y" + 81y = sec²(9x) Assuming that c1 and c2 are arbitrary constants. The general solution to the related homogeneous differential equation of: y"+81y=0 is the function: yh(x) = C1y1(x) + C2y2(x) = C1_ Assuming yp(x) is the particular solution to the differential equation: y" + 81y = sec²(9x). yp(x) is of the form yp(x) = y1(x)u1(x) + y2(x)u2(x) where; u'1(x) = & u2(x) = It follows that u1(x) = And thus yp(x) = Knowing this, the most generalized solution to the non-homogeneous differential equation y" + 81y = sec (9x) Would be: y = C1 & u2(x) = + C2

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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q35.0 You have been given the following equation. It is a non-homogeneous differential equation. y" + 81y = sec²(9x) Assuming that c1 and c2 are arbitrary constants. The general solution to the related homogeneous differential equation of: y"+81y=0 is the function : yh(x) = C1y1(x) + C2y2(x) = C1_ sec²(9x). Assuming yp(x) is the particular solution to the differential equation: y" + 81y = sec yp(x) is of the form yp(x) = y1(x)u1(x) + y2(x)u2(x) where; u'1(x) = It follows that u1(x) = And thus yp(x) = y = C1 & u2(x) + C2 & u2(x) = + C2 = Knowing this, the most generalized solution to the non-homogeneous differential equation y" + 81y = sec²(9x) Would be:
Transcribed Image Text:q35.0 You have been given the following equation. It is a non-homogeneous differential equation. y" + 81y = sec²(9x) Assuming that c1 and c2 are arbitrary constants. The general solution to the related homogeneous differential equation of: y"+81y=0 is the function : yh(x) = C1y1(x) + C2y2(x) = C1_ sec²(9x). Assuming yp(x) is the particular solution to the differential equation: y" + 81y = sec yp(x) is of the form yp(x) = y1(x)u1(x) + y2(x)u2(x) where; u'1(x) = It follows that u1(x) = And thus yp(x) = y = C1 & u2(x) + C2 & u2(x) = + C2 = Knowing this, the most generalized solution to the non-homogeneous differential equation y" + 81y = sec²(9x) Would be:
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