Solve the following differential equation:
$left parenthesis 1 minus straight x squared right parenthesis space dy space plus space straight x space straight y space dx space equals space straight x space straight y squared space dx.$

Name: Wired Faculty - The Best Learning App
Rating: 4.6 (1864 reviews)

Solution

The given differential equation is

left parenthesis 1 minus straight x squared right parenthesis space dy space plus space straight x space straight y space dx space equals space straight x space straight y squared space dx

left parenthesis 1 minus straight x squared right parenthesis space dy space equals space left parenthesis xy squared minus straight x space straight y right parenthesis space dx space space space space space space space or space space space left parenthesis 1 minus straight x squared right parenthesis space dy space equals space straight x space left parenthesis straight y squared minus straight y right parenthesis space dx

fraction numerator 1 over denominator straight y squared minus straight y end fraction dy space equals space fraction numerator straight x over denominator 1 minus straight x squared end fraction dx

therefore space space space space space integral fraction numerator 1 over denominator straight y squared minus straight y end fraction dy space equals space integral fraction numerator straight x over denominator 1 minus straight x squared end fraction dx therefore space space space space integral fraction numerator 1 over denominator straight y left parenthesis straight y minus 1 right parenthesis end fraction dy space equals space minus integral fraction numerator negative 2 straight x over denominator 1 minus straight x squared end fraction dx therefore space space integral open square brackets fraction numerator 1 over denominator straight y left parenthesis 0 minus 1 right parenthesis end fraction plus fraction numerator 1 over denominator left parenthesis 1 right parenthesis space left parenthesis straight y minus 1 right parenthesis end fraction close square brackets space dy space equals space minus integral fraction numerator negative 2 straight x over denominator 1 minus straight x squared end fraction dx therefore space integral open parentheses negative 1 over straight y plus fraction numerator 1 over denominator straight y minus 1 end fraction close parentheses space dy space equals negative integral fraction numerator negative 2 straight x over denominator 1 minus straight x squared end fraction dx therefore space space space space minus log space open vertical bar straight y close vertical bar plus space log space open vertical bar straight y minus 1 close vertical bar space equals space minus space log space open vertical bar 1 minus straight x squared close vertical bar plus space log space straight c subscript 1 therefore space log space open vertical bar fraction numerator straight y minus 1 over denominator straight y end fraction close vertical bar plus space log space open vertical bar 1 minus straight x squared close vertical bar space equals space log space straight c subscript 1 therefore space log space open vertical bar open parentheses fraction numerator straight y minus 1 over denominator straight y end fraction close parentheses space left parenthesis 1 minus straight x squared right parenthesis close vertical bar space equals space log space straight c subscript 1 space space space space space space space space space therefore space space space space open vertical bar fraction numerator left parenthesis straight y minus 1 right parenthesis thin space left parenthesis 1 minus straight x squared right parenthesis over denominator straight y end fraction close vertical bar space equals space straight c subscript 1 therefore space space space space left parenthesis straight y minus 1 right parenthesis thin space left parenthesis 1 minus straight x squared right parenthesis space equals space straight c space straight y

For Daily Free Study Material Join wiredfaculty

Vector Algebra

Solve the following differential equation:
$left parenthesis 1 minus straight x squared right parenthesis space dy space plus space straight x space straight y space dx space equals space straight x space straight y squared space dx.$

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

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Vector Algebra

Solve the following differential equation:

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 the following differential equation:
$left parenthesis 1 minus straight x squared right parenthesis space dy space plus space straight x space straight y space dx space equals space straight x space straight y squared space dx.$

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