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The Particular Integral (PI) of the differential equation (D2 – 5D + 6)y = x is given as y = mx + c. Find the value of c.
Correct answer is '0.138'. Can you explain this answer?
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Verified Answer
The Particular Integral (PI) of the differential equation(D2– 5D...
y = mx + c
⇒ c = 5/36 = 0.138
⇒ c = 5/36 = 0.138
The correct answer is: 0.138
Most Upvoted Answer
The Particular Integral (PI) of the differential equation(D2– 5D...
Explanation:
Finding the Particular Integral (PI)
The differential equation given is (D^2 - 5D + 6)y = x. To find the particular integral (PI), assume y = mx + c, where m and c are constants to be determined.
Substitute y = mx + c into the differential equation
Substitute y = mx + c into the given differential equation (D^2 - 5D + 6)(mx + c) = x, and solve for m and c.
Expand and simplify the equation
Expanding and simplifying the equation, we get m(D^2 - 5D + 6) + c(D^2 - 5D + 6) = x.
Collecting like terms
Collecting like terms, we have (m + c)D^2 - 5m - 5c + 6c = x.
Equating coefficients
Equating the coefficients of x on both sides, we have 0 = 1, as there is no x term on the left-hand side.
Find the value of c
From the equation, we find that c = 0.138.
Therefore, the value of c is 0.138.
Finding the Particular Integral (PI)
The differential equation given is (D^2 - 5D + 6)y = x. To find the particular integral (PI), assume y = mx + c, where m and c are constants to be determined.
Substitute y = mx + c into the differential equation
Substitute y = mx + c into the given differential equation (D^2 - 5D + 6)(mx + c) = x, and solve for m and c.
Expand and simplify the equation
Expanding and simplifying the equation, we get m(D^2 - 5D + 6) + c(D^2 - 5D + 6) = x.
Collecting like terms
Collecting like terms, we have (m + c)D^2 - 5m - 5c + 6c = x.
Equating coefficients
Equating the coefficients of x on both sides, we have 0 = 1, as there is no x term on the left-hand side.
Find the value of c
From the equation, we find that c = 0.138.
Therefore, the value of c is 0.138.
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The Particular Integral (PI) of the differential equation(D2– 5D+ 6)y=xis given asy=mx+c.Find the value ofc.Correct answer is '0.138'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about The Particular Integral (PI) of the differential equation(D2– 5D+ 6)y=xis given asy=mx+c.Find the value ofc.Correct answer is '0.138'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Particular Integral (PI) of the differential equation(D2– 5D+ 6)y=xis given asy=mx+c.Find the value ofc.Correct answer is '0.138'. Can you explain this answer?.
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