Solve:
x (1 + y²) dx + y (1 + x²)dy = 0

Solution

The given differential equation is
x(1 + y²) dx + y(1 + x²)dy = 0
$therefore space space space space straight y left parenthesis 1 plus straight x squared right parenthesis space dy equals space minus straight x left parenthesis 1 plus straight y squared right parenthesis space dx therefore space space space space space fraction numerator straight y over denominator 1 plus straight x squared end fraction dy space equals space minus fraction numerator straight x over denominator 1 plus straight x squared end fraction dx$
Integrating, $integral fraction numerator straight y over denominator 1 plus straight y squared end fraction dy space equals space minus integral fraction numerator straight x over denominator 1 plus straight x squared end fraction dx$
$therefore space space space space integral fraction numerator 2 straight y over denominator 1 plus straight y squared end fraction dy plus integral fraction numerator 2 straight x over denominator 1 plus straight x squared end fraction dx space equals space 0$
$therefore space space space log space left parenthesis 1 plus straight y squared right parenthesis plus space log space left parenthesis 1 plus straight x squared right parenthesis space equals space log space straight c therefore space space log space left parenthesis 1 plus straight x squared right parenthesis thin space left parenthesis 1 plus straight y squared right parenthesis space equals space log space straight c therefore space space left parenthesis 1 plus straight x squared right parenthesis thin space left parenthesis 1 plus straight y squared right parenthesis space equals straight c$
which is required solution.

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Vector Algebra

Solve:
x (1 + y²) dx + y (1 + x²)dy = 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

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Vector Algebra

Solve:x (1 + y2) dx + y (1 + x2)dy = 0

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

Solve:
x (1 + y²) dx + y (1 + x²)dy = 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