y" - 22y' + 121y = 1) Let C₁ and C₂ be arbitrary constants. The general solution to the related homogeneous differential equation y" - 22y' + 121y = 0 is the function n(x) = C₁ y ₁ (x) + C₂ Y₂ (x) = C₁ +C₂ e-11x 1+x2¹ y(0) = -10, y'(0) = 6. IOTE: The order in which you enter the answers is important; that is, C₁f(x) + C₂g(x) # C₁9(x) + C₂f(x). e-11x 1+x2 is of the form y(x) = y₁(x) u₁(x) + y₂ (x) u₂(x) where u₁(x) = = 2) The particular solution y(x) to the differential equation y" + 22y' + 121y = and u₂(x) = + 3) The most general solution to the non-homogeneous differential equation y" - 22y' + 121y = e-11x 1+x2 dt + is dt
y" - 22y' + 121y = 1) Let C₁ and C₂ be arbitrary constants. The general solution to the related homogeneous differential equation y" - 22y' + 121y = 0 is the function n(x) = C₁ y ₁ (x) + C₂ Y₂ (x) = C₁ +C₂ e-11x 1+x2¹ y(0) = -10, y'(0) = 6. IOTE: The order in which you enter the answers is important; that is, C₁f(x) + C₂g(x) # C₁9(x) + C₂f(x). e-11x 1+x2 is of the form y(x) = y₁(x) u₁(x) + y₂ (x) u₂(x) where u₁(x) = = 2) The particular solution y(x) to the differential equation y" + 22y' + 121y = and u₂(x) = + 3) The most general solution to the non-homogeneous differential equation y" - 22y' + 121y = e-11x 1+x2 dt + is dt
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
PART 3, PLEASE HIGHLIGHT THE BOXES, BARTLEBY EXPERT ANSWERS ARE WRONG
![In this exercise you will solve the initial value problem
y" 22y' + 121y =
-11x
e
1 + x²¹ y(0) = − 10, y'(0) = 6.
(1) Let C₁ and C₂ be arbitrary constants. The general solution to the related homogeneous differential equation y" - 22y' + 121y = 0 is the function
yn(x) = C₁ y₁ (x) + C₂ y₂(x) = C₁
+C₂
y =
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(x) to the differential equation y" + 22y' + 121y = is of the form y(x) = y₁(x) u₁(x) + y₂ (x) u₂(x) where u₁(x)
11x
1+x²
and u₂(x) =
(3) The most general solution to the non-homogeneous differential equation y" - 22y' + 121y =
e-11x
1+x2
dt +
is
dt](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa38b1750-4836-4d47-bfc9-b05e81f0daae%2F64fc8518-55c2-41d1-9360-7568058b8f0b%2Fa8fwp5s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In this exercise you will solve the initial value problem
y" 22y' + 121y =
-11x
e
1 + x²¹ y(0) = − 10, y'(0) = 6.
(1) Let C₁ and C₂ be arbitrary constants. The general solution to the related homogeneous differential equation y" - 22y' + 121y = 0 is the function
yn(x) = C₁ y₁ (x) + C₂ y₂(x) = C₁
+C₂
y =
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(x) to the differential equation y" + 22y' + 121y = is of the form y(x) = y₁(x) u₁(x) + y₂ (x) u₂(x) where u₁(x)
11x
1+x²
and u₂(x) =
(3) The most general solution to the non-homogeneous differential equation y" - 22y' + 121y =
e-11x
1+x2
dt +
is
dt
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Follow-up Question
PART 3, PLEASE HIGHLIGHT THE BOXES, BARTLEBY EXPERT ANSWERS ARE WRONG
![In this exercise you will solve the initial value problem
y" 22y' + 121y =
-11x
e
1 + x²¹ y(0) = − 10, y'(0) = 6.
(1) Let C₁ and C₂ be arbitrary constants. The general solution to the related homogeneous differential equation y" - 22y' + 121y = 0 is the function
yn(x) = C₁ y₁ (x) + C₂ y₂(x) = C₁
+C₂
y =
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(x) to the differential equation y" + 22y' + 121y = is of the form y(x) = y₁(x) u₁(x) + y₂ (x) u₂(x) where u₁(x)
11x
1+x²
and u₂(x) =
(3) The most general solution to the non-homogeneous differential equation y" - 22y' + 121y =
e-11x
1+x2
dt +
is
dt](https://content.bartleby.com/qna-images/question/a38b1750-4836-4d47-bfc9-b05e81f0daae/2324e012-ff8c-4791-bcb8-84f27e38de63/hr6ec8c_thumbnail.jpeg)
Transcribed Image Text:In this exercise you will solve the initial value problem
y" 22y' + 121y =
-11x
e
1 + x²¹ y(0) = − 10, y'(0) = 6.
(1) Let C₁ and C₂ be arbitrary constants. The general solution to the related homogeneous differential equation y" - 22y' + 121y = 0 is the function
yn(x) = C₁ y₁ (x) + C₂ y₂(x) = C₁
+C₂
y =
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(x) to the differential equation y" + 22y' + 121y = is of the form y(x) = y₁(x) u₁(x) + y₂ (x) u₂(x) where u₁(x)
11x
1+x²
and u₂(x) =
(3) The most general solution to the non-homogeneous differential equation y" - 22y' + 121y =
e-11x
1+x2
dt +
is
dt
Solution
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