Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > Solvea)y = (c1 + c2logx)x + logx + 2b)y = (c1...
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Solve
- a)y = (c1 + c2logx)x + logx + 2
- b)y = (c1 + c2logx)x + ex + 2
- c)y = (c1 + c2logx)x + ex logx + 2
- d)y = (c1 + c2x)log x + log x + 2
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Solvea)y = (c1 + c2logx)x + logx + 2b)y = (c1 + c2logx)x + ex + 2c)y =...
Explanation:
Linear differential equations with variable coefficients which can be reduced to linear differential equations with constant coefficients by suitable substitution.
Euler Cauchy's homogeneous linear equation:
This is a Cauchy’s homogenous linear equation
This is a Cauchy’s homogenous linear equation
Put x = et
⇒ t = log x
Now, the equation becomes,
Now, the equation becomes,
(D(D − 1) − D + 1)y = t ⇒ (D − 1)2y = t
A.E. is (D – 1)2 = 0
⇒ D = 1, 1
C.F. = (c1 + c2 t) et
= t + 2
= t + 2
Complete solution is
y = (c1 + c2 t) et + t + 2
Putting t = log x
⇒ y = (c1 + c2 log x) x + log x + 2
Most Upvoted Answer
Solvea)y = (c1 + c2logx)x + logx + 2b)y = (c1 + c2logx)x + ex + 2c)y =...
Explanation:
Linear differential equations with variable coefficients which can be reduced to linear differential equations with constant coefficients by suitable substitution.
Euler Cauchy's homogeneous linear equation:
This is a Cauchy’s homogenous linear equation
This is a Cauchy’s homogenous linear equation
Put x = et
⇒ t = log x
Now, the equation becomes,
Now, the equation becomes,
(D(D − 1) − D + 1)y = t ⇒ (D − 1)2y = t
A.E. is (D – 1)2 = 0
⇒ D = 1, 1
C.F. = (c1 + c2 t) et
= t + 2
= t + 2
Complete solution is
y = (c1 + c2 t) et + t + 2
Putting t = log x
⇒ y = (c1 + c2 log x) x + log x + 2
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Solvea)y = (c1 + c2logx)x + logx + 2b)y = (c1 + c2logx)x + ex + 2c)y = (c1 + c2logx)x + exlogx+ 2d)y = (c1 + c2x)log x + log x+ 2Correct answer is option 'A'. Can you explain this answer?
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Solvea)y = (c1 + c2logx)x + logx + 2b)y = (c1 + c2logx)x + ex + 2c)y = (c1 + c2logx)x + exlogx+ 2d)y = (c1 + c2x)log x + log x+ 2Correct answer is option 'A'. 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 Solvea)y = (c1 + c2logx)x + logx + 2b)y = (c1 + c2logx)x + ex + 2c)y = (c1 + c2logx)x + exlogx+ 2d)y = (c1 + c2x)log x + log x+ 2Correct answer is option 'A'. 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 Solvea)y = (c1 + c2logx)x + logx + 2b)y = (c1 + c2logx)x + ex + 2c)y = (c1 + c2logx)x + exlogx+ 2d)y = (c1 + c2x)log x + log x+ 2Correct answer is option 'A'. Can you explain this answer?.
Solvea)y = (c1 + c2logx)x + logx + 2b)y = (c1 + c2logx)x + ex + 2c)y = (c1 + c2logx)x + exlogx+ 2d)y = (c1 + c2x)log x + log x+ 2Correct answer is option 'A'. 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 Solvea)y = (c1 + c2logx)x + logx + 2b)y = (c1 + c2logx)x + ex + 2c)y = (c1 + c2logx)x + exlogx+ 2d)y = (c1 + c2x)log x + log x+ 2Correct answer is option 'A'. 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 Solvea)y = (c1 + c2logx)x + logx + 2b)y = (c1 + c2logx)x + ex + 2c)y = (c1 + c2logx)x + exlogx+ 2d)y = (c1 + c2x)log x + log x+ 2Correct answer is option 'A'. Can you explain this answer?.
Solutions for Solvea)y = (c1 + c2logx)x + logx + 2b)y = (c1 + c2logx)x + ex + 2c)y = (c1 + c2logx)x + exlogx+ 2d)y = (c1 + c2x)log x + log x+ 2Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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