Find the general solution of each of the following equations:
$dy over dx equals fraction numerator straight y left parenthesis straight x squared minus 1 right parenthesis over denominator straight x left parenthesis straight y squared minus 1 right parenthesis end fraction$

Solution

The given differential equation is
$dy over dx space equals space fraction numerator straight y left parenthesis straight x squared minus 1 right parenthesis over denominator straight x left parenthesis straight y squared minus 1 right parenthesis end fraction$
Separating the variables, we get,
$fraction numerator straight y squared minus 1 over denominator straight y end fraction dy space equals space fraction numerator straight x squared minus 1 over denominator straight x end fraction dx$
$therefore space space space space space space integral open parentheses straight y squared over straight y minus 1 over straight y close parentheses dy space equals space integral open parentheses straight x squared over straight x minus 1 over straight x close parentheses dx$
or $integral open parentheses straight y minus 1 over straight y close parentheses dy space equals space integral open parentheses straight x minus 1 over straight x close parentheses dx$
or $straight y squared over 2 minus log space open vertical bar straight y close vertical bar space equals space straight x squared over 2 minus log space open vertical bar straight x close vertical bar space plus space straight c$
is the required solution.

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Vector Algebra

Find the general solution of each of the following equations:
$dy over dx equals fraction numerator straight y left parenthesis straight x squared minus 1 right parenthesis over denominator straight x left parenthesis straight y squared minus 1 right parenthesis end fraction$

Some More Questions From Vector Algebra Chapter

Determine order and degree (if defined) of differential equations:
y' + y = e^x

Determine order and degree (if defined) of differential equations:
y'' + (y')² + 2 y = 0

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Vector Algebra

Find the general solution of each of the following equations:

Some More Questions From Vector Algebra Chapter

Determine order and degree (if defined) of differential equations:y' + y = ex

Determine order and degree (if defined) of differential equations:y'' + (y')2 + 2 y = 0

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find the general solution of each of the following equations:
$dy over dx equals fraction numerator straight y left parenthesis straight x squared minus 1 right parenthesis over denominator straight x left parenthesis straight y squared minus 1 right parenthesis end fraction$

Determine order and degree (if defined) of differential equations:
y' + y = e^x

Determine order and degree (if defined) of differential equations:
y'' + (y')² + 2 y = 0