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y = A ex + B e2x + C e3x satisfies the diferential equation
- a)y ‴ − 6 y ″ + 11 y ′ − 6 y = 0
- b)y ‴ + 6 y ″ + 11 y ′ + 6 y = 0
- c)y ‴ + 6 y ″ − 11 y ′ + 6 y = 0
- d)y ‴ − 6 y ″ − 11 y ′ + 6 y = 0
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
y = A ex + B e2x + C e3xsatisfies the diferential equationa)y −...
Given Information:
The function y = Aex + Be2x + Ce3x satisfies the differential equation y'' - 6y' + 11y' - 6y = 0.
Explanation:
Step 1: Find y', y''
Given y = Aex + Be2x + Ce3x, we can find y' and y'' by taking the derivatives:
y' = Aex + 2Be2x + 3Ce3x
y'' = Aex + 4Be2x + 9Ce3x
Step 2: Substitute y, y', y'' into the differential equation
Now, substitute y, y', y'' into the given differential equation:
y'' - 6y' + 11y' - 6y = 0
(Aex + 4Be2x + 9Ce3x) - 6(Aex + 2Be2x + 3Ce3x) + 11(Aex + 2Be2x + 3Ce3x) - 6(Aex + Be2x + Ce3x) = 0
Step 3: Simplify the expression
After simplifying the above expression, we get:
(A - 6A + 11A - 6A)ex + (4B - 12B + 22B - 6B)e2x + (9C - 18C + 33C - 6C)e3x = 0
(-6A)e2x + (8B)e2x + (18C)e3x = 0
Step 4: Equate coefficients to zero
Now, equate the coefficients of ex, e2x, e3x to zero:
-6A = 0
8B - 12B = 0
18C = 0
From the above, we get A = 0, B = 0, C = 0.
Therefore, the function y = Aex + Be2x + Ce3x satisfies the differential equation y'' - 6y' + 11y' - 6y = 0, which corresponds to option A.
The function y = Aex + Be2x + Ce3x satisfies the differential equation y'' - 6y' + 11y' - 6y = 0.
Explanation:
Step 1: Find y', y''
Given y = Aex + Be2x + Ce3x, we can find y' and y'' by taking the derivatives:
y' = Aex + 2Be2x + 3Ce3x
y'' = Aex + 4Be2x + 9Ce3x
Step 2: Substitute y, y', y'' into the differential equation
Now, substitute y, y', y'' into the given differential equation:
y'' - 6y' + 11y' - 6y = 0
(Aex + 4Be2x + 9Ce3x) - 6(Aex + 2Be2x + 3Ce3x) + 11(Aex + 2Be2x + 3Ce3x) - 6(Aex + Be2x + Ce3x) = 0
Step 3: Simplify the expression
After simplifying the above expression, we get:
(A - 6A + 11A - 6A)ex + (4B - 12B + 22B - 6B)e2x + (9C - 18C + 33C - 6C)e3x = 0
(-6A)e2x + (8B)e2x + (18C)e3x = 0
Step 4: Equate coefficients to zero
Now, equate the coefficients of ex, e2x, e3x to zero:
-6A = 0
8B - 12B = 0
18C = 0
From the above, we get A = 0, B = 0, C = 0.
Therefore, the function y = Aex + Be2x + Ce3x satisfies the differential equation y'' - 6y' + 11y' - 6y = 0, which corresponds to option A.
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y = A ex + B e2x + C e3xsatisfies the diferential equationa)y − 6 y ″ + 11 y ′ − 6 y = 0b)y + 6 y ″ + 11 y ′ + 6 y = 0c)y + 6 y ″ − 11 y ′ + 6 y = 0d)y − 6 y ″ − 11 y ′ + 6 y = 0Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about y = A ex + B e2x + C e3xsatisfies the diferential equationa)y − 6 y ″ + 11 y ′ − 6 y = 0b)y + 6 y ″ + 11 y ′ + 6 y = 0c)y + 6 y ″ − 11 y ′ + 6 y = 0d)y − 6 y ″ − 11 y ′ + 6 y = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for y = A ex + B e2x + C e3xsatisfies the diferential equationa)y − 6 y ″ + 11 y ′ − 6 y = 0b)y + 6 y ″ + 11 y ′ + 6 y = 0c)y + 6 y ″ − 11 y ′ + 6 y = 0d)y − 6 y ″ − 11 y ′ + 6 y = 0Correct answer is option 'A'. Can you explain this answer?.
y = A ex + B e2x + C e3xsatisfies the diferential equationa)y − 6 y ″ + 11 y ′ − 6 y = 0b)y + 6 y ″ + 11 y ′ + 6 y = 0c)y + 6 y ″ − 11 y ′ + 6 y = 0d)y − 6 y ″ − 11 y ′ + 6 y = 0Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about y = A ex + B e2x + C e3xsatisfies the diferential equationa)y − 6 y ″ + 11 y ′ − 6 y = 0b)y + 6 y ″ + 11 y ′ + 6 y = 0c)y + 6 y ″ − 11 y ′ + 6 y = 0d)y − 6 y ″ − 11 y ′ + 6 y = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for y = A ex + B e2x + C e3xsatisfies the diferential equationa)y − 6 y ″ + 11 y ′ − 6 y = 0b)y + 6 y ″ + 11 y ′ + 6 y = 0c)y + 6 y ″ − 11 y ′ + 6 y = 0d)y − 6 y ″ − 11 y ′ + 6 y = 0Correct answer is option 'A'. Can you explain this answer?.
Solutions for y = A ex + B e2x + C e3xsatisfies the diferential equationa)y − 6 y ″ + 11 y ′ − 6 y = 0b)y + 6 y ″ + 11 y ′ + 6 y = 0c)y + 6 y ″ − 11 y ′ + 6 y = 0d)y − 6 y ″ − 11 y ′ + 6 y = 0Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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