20.11. For each of the following, state the appropriate guess for the form for a particular solution yp(x). This 'guess' should be the one that works, not necessarily the first. Leave the coefficients 'undetermined’; that is, do NOT actually determine the values of the coefficients. а. у" — 4y' + 5у — х*е * sin(x) b. у" — 4y' + 5у %3D х3е2r sin(x) с. у" 5y' + бу = x²e-7x + 2e-7x d. y" — 5y' + бу з — х2 = x? e. y" 5y' + 6y = 4e-&r 4e-8r г. у" — 5у' + бу g. у" — 5у' + бу 4e3r - h. 5y' + 6y x? cos(2x) - i. y" 5y' + 6y= X*e* sin(2x) j. y" 1. y" 4y' + 20y = e* sin(2x) k. 4у + 20y 3 e2x sin(4x) m. y" 10y' + 25у 4y' + 20y = x' sin(4x) 3x²e5x п. у" 10y' + 25у 3x4 %3D 20.12. Find particular solutions to the following differential equations. For your convenience, yh , the solution to the corresponding homogeneous equation (which you found in chapter 17) is also given for each differential equation. y(4) – 4y(3) а. = 12e-2x Yh (x) = c1 + c2x + c3x² + c4e* b. y(4) 4y(3) 10 sin(2x) , - Yh (x) = c1 + c2x + c3x² + c4e4x с. y(4) 4y(3) 32e4* Yh (x) = c1 + c2x + c3x² + c4eªx d. y(4) 4y(3) = 32x - Yh (x) = c1 + c2x + c3x² + c4eª* y(3) - y" + y' – y = x² е. Yh (x) = cje* + c2 cos(x) + C3 sin(x) f. y" + y' - y = 30 cos(2x) , Yh(x) = p(3) cje* + c2 cos(x) + c3 sin(x) Yh (x) = cje* + c2 cos(x) + c3 sin(x) p(3) y" + y' - y = 6e* g.
20.11. For each of the following, state the appropriate guess for the form for a particular solution yp(x). This 'guess' should be the one that works, not necessarily the first. Leave the coefficients 'undetermined’; that is, do NOT actually determine the values of the coefficients. а. у" — 4y' + 5у — х*е * sin(x) b. у" — 4y' + 5у %3D х3е2r sin(x) с. у" 5y' + бу = x²e-7x + 2e-7x d. y" — 5y' + бу з — х2 = x? e. y" 5y' + 6y = 4e-&r 4e-8r г. у" — 5у' + бу g. у" — 5у' + бу 4e3r - h. 5y' + 6y x? cos(2x) - i. y" 5y' + 6y= X*e* sin(2x) j. y" 1. y" 4y' + 20y = e* sin(2x) k. 4у + 20y 3 e2x sin(4x) m. y" 10y' + 25у 4y' + 20y = x' sin(4x) 3x²e5x п. у" 10y' + 25у 3x4 %3D 20.12. Find particular solutions to the following differential equations. For your convenience, yh , the solution to the corresponding homogeneous equation (which you found in chapter 17) is also given for each differential equation. y(4) – 4y(3) а. = 12e-2x Yh (x) = c1 + c2x + c3x² + c4e* b. y(4) 4y(3) 10 sin(2x) , - Yh (x) = c1 + c2x + c3x² + c4e4x с. y(4) 4y(3) 32e4* Yh (x) = c1 + c2x + c3x² + c4eªx d. y(4) 4y(3) = 32x - Yh (x) = c1 + c2x + c3x² + c4eª* y(3) - y" + y' – y = x² е. Yh (x) = cje* + c2 cos(x) + C3 sin(x) f. y" + y' - y = 30 cos(2x) , Yh(x) = p(3) cje* + c2 cos(x) + c3 sin(x) Yh (x) = cje* + c2 cos(x) + c3 sin(x) p(3) y" + y' - y = 6e* g.
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...
Related questions
Question
Please solve both 11H and 12F
Transcribed Image Text:20.11. For each of the following, state the appropriate guess for the form for a particular solution
yp(x). This guess' should be the one that works, not necessarily the first. Leave the
coefficients 'undetermined; that is, do NOT actually determine the values of the coefficients.
а. у" — 4у + 5у
x³e¯* sin(x)
b. у" — 4у' + 5у
x'e2x sin(x)
-
с. у"
5y' + бу
= x?e-7x + 2e-7x
-
d. y" — 5y' + бу — х2
e. y"
5y' + 6y = 4e¬8x
-
f. y"
5y + бу
4e3x
-
g. у" — 5у' + бу
-
h.) y"
5y + 6у
x² cos(2x)
-
i. y"
5y' + 6= x e* sin(2x)
-
j. y"
4y' + 20y
= e4* sin(2x)
k. y".
4y' + 20y
= e2* sin(4x)
1. y"
4y' + 20y
= x' sin(4x)
-
m. y"
10y + 25у
3x²e5x
п. у" — 10у' + 25у
3x4
20.12. Find particular solutions to the following differential equations. For your convenience, yh ,
the solution to the corresponding homogeneous equation (which you found in chapter 17)
is also given for each differential equation.
а. у) — 4у3)
y
12e
12e-2x
Yh (x) = c1 + c2x + c3x² + ¢4e%*
b. y(4) – 4y(3)
= 10 sin(2x)
-
Yh (x) = c1 + c2x + c3x² + c4e4x
4y(3)
= 32e4x
с.
p(4)
-
Yh (x) = c1 + c2x + c3x² + c4e%x
d.
y(4)
4y(3)
= 32x
Yh (x) = c1 + c2x + c3x² + c4e+*
y(3)
y" + y' – y = x² ,
е.
Yh (x) = cje* + c2 cos(x) + C3 sin(x)
f.
Þ(3)
y" + y'
y = 30 cos(2.x)
yh (x) = cje* + c2 cos(x) + c3 sin(x)
g. y(3)
- у" + у' — у%3D бе"
Уп (х)
cje* + c2 cos(x) + c3 sin(x)
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