Solve by variable separation method.
in Other Math Topics by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

QUESTION: (x+1) dy/dx= x (y^2+1)

Solve by variable separation method.

put all the y's on the left anf all the x's on the right.

dy/(y^2+1) = x.dx/(x+1)

now integrate both sides.

Int 1/(y^2+1) dy = Int x/(x+1) dx

LHS

Int 1/(y^2+1) dy = atan(y)

RHS

Int x/(x+1) dx = Int 1 - 1/(x+1) dx = x - ln(x+1) - lnA   (lnA = const of integration)

Int x/(x+1) dx = x - ln(A(x+1))

Equating both sides,

atan(y) = x - ln(A(x+1))

y = tan{x - ln(A(x+1))}

by Level 11 User (80.8k points)

Related questions

1 answer
asked Sep 17, 2013 in Calculus Answers by mermaid_raid Level 1 User (120 points) | 175 views
1 answer
asked Jun 15, 2013 in Calculus Answers by anonymous | 353 views
0 answers
1 answer
asked Mar 17, 2013 in Algebra 2 Answers by anonymous | 170 views
0 answers
1 answer
asked Sep 16, 2012 in Calculus Answers by anonymous | 1.4k views
1 answer
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
83,155 questions
87,984 answers
1,978 comments
4,874 users