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General solution of the Cauchy-Euler equation
- a)y = c1x2 + c2x4
- b)y = c1x2 + c2x-4
- c)y = (c1 + c2 In x) x4
- d)y = c1x4 + c2x-4 In x
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
General solution of the Cauchy-Euler equationa)y = c1x2+ c2x4b)y = c1x...
Concept:
For different roots of the auxiliary equation, the solution (complementary function) of the differential equation is as shown below.
Calculation:
Calculation:
Given:
Put x = et
Put x = et
⇒ t = ln x
Now, the above differential equation becomes
Now, the above differential equation becomes
D(D – 1)y – 7Dy + 16y = 0
⇒ D2y – Dy – 7Dy + 16y = 0
⇒ (D2 – 8D + 16)y = 0
Auxiliary equation:
(D2 – 8 D + 16) = 0
⇒ D = 4
The solutions for the above roots of auxiliary equations are:
y(t) = (c1 + c2 t) e4t
⇒ y(x) = (c1 + c2 ln x) x4
Most Upvoted Answer
General solution of the Cauchy-Euler equationa)y = c1x2+ c2x4b)y = c1x...
Concept:
For different roots of the auxiliary equation, the solution (complementary function) of the differential equation is as shown below.
Calculation:
Calculation:
Given:
Put x = et
Put x = et
⇒ t = ln x
Now, the above differential equation becomes
Now, the above differential equation becomes
D(D – 1)y – 7Dy + 16y = 0
⇒ D2y – Dy – 7Dy + 16y = 0
⇒ (D2 – 8D + 16)y = 0
Auxiliary equation:
(D2 – 8 D + 16) = 0
⇒ D = 4
The solutions for the above roots of auxiliary equations are:
y(t) = (c1 + c2 t) e4t
⇒ y(x) = (c1 + c2 ln x) x4
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General solution of the Cauchy-Euler equationa)y = c1x2+ c2x4b)y = c1x2+ c2x-4c)y = (c1+ c2In x) x4d)y = c1x4+ c2x-4In xCorrect answer is option 'C'. Can you explain this answer?
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General solution of the Cauchy-Euler equationa)y = c1x2+ c2x4b)y = c1x2+ c2x-4c)y = (c1+ c2In x) x4d)y = c1x4+ c2x-4In xCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about General solution of the Cauchy-Euler equationa)y = c1x2+ c2x4b)y = c1x2+ c2x-4c)y = (c1+ c2In x) x4d)y = c1x4+ c2x-4In xCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for General solution of the Cauchy-Euler equationa)y = c1x2+ c2x4b)y = c1x2+ c2x-4c)y = (c1+ c2In x) x4d)y = c1x4+ c2x-4In xCorrect answer is option 'C'. Can you explain this answer?.
General solution of the Cauchy-Euler equationa)y = c1x2+ c2x4b)y = c1x2+ c2x-4c)y = (c1+ c2In x) x4d)y = c1x4+ c2x-4In xCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about General solution of the Cauchy-Euler equationa)y = c1x2+ c2x4b)y = c1x2+ c2x-4c)y = (c1+ c2In x) x4d)y = c1x4+ c2x-4In xCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for General solution of the Cauchy-Euler equationa)y = c1x2+ c2x4b)y = c1x2+ c2x-4c)y = (c1+ c2In x) x4d)y = c1x4+ c2x-4In xCorrect answer is option 'C'. Can you explain this answer?.
Solutions for General solution of the Cauchy-Euler equationa)y = c1x2+ c2x4b)y = c1x2+ c2x-4c)y = (c1+ c2In x) x4d)y = c1x4+ c2x-4In xCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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