Problem #2: Let Problem #2: L[v] = any(n)(x) + an-1.y(n − ¹)(x) + ... + α₁ y'(x) + 㵂y(x), where ao. a1,..., an are fixed constants. Consider the nth order linear differential equation L[y] (16+ 12x - 12x²) e³x If it is known that L[v₁(x)] = (4-3x²) e³x when L[1₂ (x)] -3.xe3x when = (*) Find a particular solution, yp(x), to (*). y₁(x) = (2-3x + 3.x²) e³x 2(x) = (4 + 2x - 3x²) e³x Enter your answer as a symbolic function of x, as in these examples Do not include 'y = in your answer.
Problem #2: Let Problem #2: L[v] = any(n)(x) + an-1.y(n − ¹)(x) + ... + α₁ y'(x) + 㵂y(x), where ao. a1,..., an are fixed constants. Consider the nth order linear differential equation L[y] (16+ 12x - 12x²) e³x If it is known that L[v₁(x)] = (4-3x²) e³x when L[1₂ (x)] -3.xe3x when = (*) Find a particular solution, yp(x), to (*). y₁(x) = (2-3x + 3.x²) e³x 2(x) = (4 + 2x - 3x²) e³x Enter your answer as a symbolic function of x, as in these examples Do not include 'y = in your answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Problem #2: Let
Problem #2:
L[v] = any (n)(x) + an−1 y(n − ¹)(x) + ... + a₁ y'(x) + ay(x),
where ao, a₁,..., an are fixed constants. Consider the nth order linear differential equation
Jury
L[v] (16+ 12x12x²) e³x
If it is known that
L[v₁ (x)] = (4-3x²) e³x when
L[v2(r)] = –3re3t
when
Find a particular solution, yp(x), to (*).
y₁(x) = (2-3x+3x²) e³x
y(x) = (4 + 2x - 3x²) e³x
Enter your answer as a symbolic
function of x, as in these
examples
Do not include 'y = 'in your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd3c3147-011e-442a-8bf9-af3591b7ce73%2Fba7772f9-1b33-4cf2-8561-f27f2afef798%2Fhbzfurb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem #2: Let
Problem #2:
L[v] = any (n)(x) + an−1 y(n − ¹)(x) + ... + a₁ y'(x) + ay(x),
where ao, a₁,..., an are fixed constants. Consider the nth order linear differential equation
Jury
L[v] (16+ 12x12x²) e³x
If it is known that
L[v₁ (x)] = (4-3x²) e³x when
L[v2(r)] = –3re3t
when
Find a particular solution, yp(x), to (*).
y₁(x) = (2-3x+3x²) e³x
y(x) = (4 + 2x - 3x²) e³x
Enter your answer as a symbolic
function of x, as in these
examples
Do not include 'y = 'in your answer.
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