Question

Solve:
$straight x squared left parenthesis straight y minus 1 right parenthesis space dx space plus space straight y squared space left parenthesis straight x minus 1 right parenthesis space dy space equals space 0$

Solution

The given differential equation is
$straight x squared left parenthesis straight y minus 1 right parenthesis space dx space plus space straight y squared left parenthesis straight x minus 1 right parenthesis space dy space equals space 0 space space or space space straight y squared left parenthesis straight x minus 1 right parenthesis space dy space equals space minus straight x squared left parenthesis straight y minus 1 right parenthesis space dx$
or $fraction numerator straight y squared over denominator straight y minus 1 end fraction dy space equals space minus fraction numerator straight x squared over denominator straight x minus 1 end fraction dx$
Integrating, $integral fraction numerator straight y squared over denominator straight y minus 1 end fraction dy space equals space minus integral fraction numerator straight x squared over denominator straight x minus 1 end fraction dx$
$therefore space space space space space integral open parentheses straight y plus 1 plus fraction numerator 1 over denominator straight y minus 1 end fraction close parentheses dy space equals space minus integral open parentheses straight x plus 1 plus fraction numerator 1 over denominator straight x minus 1 end fraction close parentheses dx therefore space space straight y squared over 2 plus straight y plus log space open vertical bar straight y minus 1 close vertical bar space equals space minus open square brackets straight x squared over 2 plus straight x plus log space open vertical bar straight x plus 1 close vertical bar close square brackets plus straight c$
is the required solution.

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Vector Algebra

Solve:
$straight x squared left parenthesis straight y minus 1 right parenthesis space dx space plus space straight y squared space left parenthesis straight x minus 1 right parenthesis space dy space equals space 0$

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

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

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Vector Algebra

Solve:

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

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

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Solve:
$straight x squared left parenthesis straight y minus 1 right parenthesis space dx space plus space straight y squared space left parenthesis straight x minus 1 right parenthesis space dy space equals space 0$

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

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