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
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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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:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0231177e-a94f-4371-be99-2d02d3dc9a19%2F642d2c95-b013-4af4-a7f4-9e44665a79ac%2Fw2qnzg_processed.png&w=3840&q=75)
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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