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The solution of differential equation un+3 - 4un+2 + un+1 + 6un = 0 will be:
- a)un = C1(1)n + C2(2)n + C3(3)n, where C1, C2, C3 are constants.
- b)un = C1(-1)n +C2(-2)n + C3(-3)n, where C1, C2, C3 are constants.
- c)un = C1(1)n + C2(-2)n + C3(3)n, where C1, C2, C3 are constants.
- d)un = C1 (-1)n + C2(2)n + C3(3)n, where C1, C2, C3 are constants.
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The solution of differential equation un+3- 4un+2+ un+1+ 6un= 0 will b...
Concept:
For solving a homogeneous linear differential equation with constant coefficients,
As a solution, we try un = A mn, where A and m are constants.
This choice has been made because un = kn uo was the solution to the equation un = k un-1.
After substituting and solving the auxiliary equation, say m1, m2, m3 ... mn be the roots, then the general solution will be
un = A(m1)n + B(m2)n + ... where A, B ... are constants
For solving a homogeneous linear differential equation with constant coefficients,
As a solution, we try un = A mn, where A and m are constants.
This choice has been made because un = kn uo was the solution to the equation un = k un-1.
After substituting and solving the auxiliary equation, say m1, m2, m3 ... mn be the roots, then the general solution will be
un = A(m1)n + B(m2)n + ... where A, B ... are constants
Calculation:
Given Differential equation is:
un+3 - 4n+2 + un+1 + 6un = 0
Substituting:
un+3 = A mn+3;
un+2 = A mn+2;
un+1 = A mn+1;
un = A mn;
A mn+3 - 4 A mn+2 + A mn+1 + 6 A mn = 0
A mn (m3 - 4m2 + m + 6) = 0
m3 - 4m2 + m + 6 = 0
This is called auxiliary equation.
The roots of the auxiliary equation are -1, 2, and 3, i.e.
m1 = -1, m2 = 2, m3 = 3;
The general solution will be:
un = A(-1)n + B(2)n + C(3)n
Given Differential equation is:
un+3 - 4n+2 + un+1 + 6un = 0
Substituting:
un+3 = A mn+3;
un+2 = A mn+2;
un+1 = A mn+1;
un = A mn;
A mn+3 - 4 A mn+2 + A mn+1 + 6 A mn = 0
A mn (m3 - 4m2 + m + 6) = 0
m3 - 4m2 + m + 6 = 0
This is called auxiliary equation.
The roots of the auxiliary equation are -1, 2, and 3, i.e.
m1 = -1, m2 = 2, m3 = 3;
The general solution will be:
un = A(-1)n + B(2)n + C(3)n
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The solution of differential equation un+3- 4un+2+ un+1+ 6un= 0 will be:a)un= C1(1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.b)un= C1(-1)n+C2(-2)n+ C3(-3)n, where C1, C2, C3are constants.c)un= C1(1)n+ C2(-2)n+ C3(3)n, where C1, C2, C3are constants.d)un= C1(-1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.Correct answer is option 'D'. Can you explain this answer?
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The solution of differential equation un+3- 4un+2+ un+1+ 6un= 0 will be:a)un= C1(1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.b)un= C1(-1)n+C2(-2)n+ C3(-3)n, where C1, C2, C3are constants.c)un= C1(1)n+ C2(-2)n+ C3(3)n, where C1, C2, C3are constants.d)un= C1(-1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.Correct answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The solution of differential equation un+3- 4un+2+ un+1+ 6un= 0 will be:a)un= C1(1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.b)un= C1(-1)n+C2(-2)n+ C3(-3)n, where C1, C2, C3are constants.c)un= C1(1)n+ C2(-2)n+ C3(3)n, where C1, C2, C3are constants.d)un= C1(-1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The solution of differential equation un+3- 4un+2+ un+1+ 6un= 0 will be:a)un= C1(1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.b)un= C1(-1)n+C2(-2)n+ C3(-3)n, where C1, C2, C3are constants.c)un= C1(1)n+ C2(-2)n+ C3(3)n, where C1, C2, C3are constants.d)un= C1(-1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.Correct answer is option 'D'. Can you explain this answer?.
The solution of differential equation un+3- 4un+2+ un+1+ 6un= 0 will be:a)un= C1(1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.b)un= C1(-1)n+C2(-2)n+ C3(-3)n, where C1, C2, C3are constants.c)un= C1(1)n+ C2(-2)n+ C3(3)n, where C1, C2, C3are constants.d)un= C1(-1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.Correct answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The solution of differential equation un+3- 4un+2+ un+1+ 6un= 0 will be:a)un= C1(1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.b)un= C1(-1)n+C2(-2)n+ C3(-3)n, where C1, C2, C3are constants.c)un= C1(1)n+ C2(-2)n+ C3(3)n, where C1, C2, C3are constants.d)un= C1(-1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The solution of differential equation un+3- 4un+2+ un+1+ 6un= 0 will be:a)un= C1(1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.b)un= C1(-1)n+C2(-2)n+ C3(-3)n, where C1, C2, C3are constants.c)un= C1(1)n+ C2(-2)n+ C3(3)n, where C1, C2, C3are constants.d)un= C1(-1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.Correct answer is option 'D'. Can you explain this answer?.
Solutions for The solution of differential equation un+3- 4un+2+ un+1+ 6un= 0 will be:a)un= C1(1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.b)un= C1(-1)n+C2(-2)n+ C3(-3)n, where C1, C2, C3are constants.c)un= C1(1)n+ C2(-2)n+ C3(3)n, where C1, C2, C3are constants.d)un= C1(-1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
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The solution of differential equation un+3- 4un+2+ un+1+ 6un= 0 will be:a)un= C1(1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.b)un= C1(-1)n+C2(-2)n+ C3(-3)n, where C1, C2, C3are constants.c)un= C1(1)n+ C2(-2)n+ C3(3)n, where C1, C2, C3are constants.d)un= C1(-1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for The solution of differential equation un+3- 4un+2+ un+1+ 6un= 0 will be:a)un= C1(1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.b)un= C1(-1)n+C2(-2)n+ C3(-3)n, where C1, C2, C3are constants.c)un= C1(1)n+ C2(-2)n+ C3(3)n, where C1, C2, C3are constants.d)un= C1(-1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of The solution of differential equation un+3- 4un+2+ un+1+ 6un= 0 will be:a)un= C1(1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.b)un= C1(-1)n+C2(-2)n+ C3(-3)n, where C1, C2, C3are constants.c)un= C1(1)n+ C2(-2)n+ C3(3)n, where C1, C2, C3are constants.d)un= C1(-1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The solution of differential equation un+3- 4un+2+ un+1+ 6un= 0 will be:a)un= C1(1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.b)un= C1(-1)n+C2(-2)n+ C3(-3)n, where C1, C2, C3are constants.c)un= C1(1)n+ C2(-2)n+ C3(3)n, where C1, C2, C3are constants.d)un= C1(-1)n+ C2(2)n+ C3(3)n, where C1, C2, C3are constants.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
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