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Consider the following differential equation:
Which of the following is the solution of the above equation (c is an arbitrary constant)?
- a)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Consider the following differential equation:Which of the following is...
Divide both the sides by (x^2) dx
All the terms are now in the form of (y/x) and dy/dx
Now put (y/x)=v
so that dy/dx = v+x(dv/dx). | by product rule
simplifying it you'll get something like this
(dv/dx) = (2v*cosv)/(vsinv - cosv)
[ (vsinv - cosv)/2vcosv] dv = dx/x
simplifying some more
[ ( tanv/2) - 1/2v ] dv = dx/x
Now integrate simply and you'll get
(1/2) [ log|secv| - logv ] = log x + log c
simplify it (1/2) [ log(secv/v) ] = log(cx)
log √(secv/v) = log (cx)
√(secv/v) = cx
secv/v = (cx)square
since c^2 is also a constant you can take it as other constant say c again
[ 1/vcosv ] = cx^2
[ x/ycos(y/x) ] = cx^2
now 1/c will again be a constant and I'm taking it as 'c' again
xycos(y/x) = c
All the terms are now in the form of (y/x) and dy/dx
Now put (y/x)=v
so that dy/dx = v+x(dv/dx). | by product rule
simplifying it you'll get something like this
(dv/dx) = (2v*cosv)/(vsinv - cosv)
[ (vsinv - cosv)/2vcosv] dv = dx/x
simplifying some more
[ ( tanv/2) - 1/2v ] dv = dx/x
Now integrate simply and you'll get
(1/2) [ log|secv| - logv ] = log x + log c
simplify it (1/2) [ log(secv/v) ] = log(cx)
log √(secv/v) = log (cx)
√(secv/v) = cx
secv/v = (cx)square
since c^2 is also a constant you can take it as other constant say c again
[ 1/vcosv ] = cx^2
[ x/ycos(y/x) ] = cx^2
now 1/c will again be a constant and I'm taking it as 'c' again
xycos(y/x) = c
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Consider the following differential equation:Which of the following is the solution of the above equation (c is an arbitrary constant)?a)b)c)d)Correct answer is option 'C'. Can you explain this answer?
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Consider the following differential equation:Which of the following is the solution of the above equation (c is an arbitrary constant)?a)b)c)d)Correct 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 Consider the following differential equation:Which of the following is the solution of the above equation (c is an arbitrary constant)?a)b)c)d)Correct 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 Consider the following differential equation:Which of the following is the solution of the above equation (c is an arbitrary constant)?a)b)c)d)Correct answer is option 'C'. Can you explain this answer?.
Consider the following differential equation:Which of the following is the solution of the above equation (c is an arbitrary constant)?a)b)c)d)Correct 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 Consider the following differential equation:Which of the following is the solution of the above equation (c is an arbitrary constant)?a)b)c)d)Correct 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 Consider the following differential equation:Which of the following is the solution of the above equation (c is an arbitrary constant)?a)b)c)d)Correct answer is option 'C'. Can you explain this answer?.
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