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Vector Algebra

Question
CBSEENMA12033025
Wired Faculty App

Solve the following differential equation:
dy over dx space equals space 1 plus straight x plus straight y plus xy comma space space straight y greater than 0

            

Solution
The given differential equation is
                      dy over dx equals 1 plus straight x plus straight y plus xy space space or space space space dy over dx space equals space left parenthesis 1 plus straight x right parenthesis space plus straight y left parenthesis 1 plus straight x right parenthesis
or             dy over dx space equals left parenthesis 1 plus straight x right parenthesis space left parenthesis 1 plus straight y right parenthesis
Separating the variables, we get,  fraction numerator 1 over denominator 1 plus straight y end fraction dy space equals space left parenthesis 1 plus straight x right parenthesis space dx comma space space space space or space space space integral fraction numerator dy over denominator 1 plus straight y end fraction space equals space integral left parenthesis 1 plus straight x right parenthesis space dx
therefore space space log space left parenthesis 1 plus straight y right parenthesis space equals space fraction numerator left parenthesis 1 plus straight x right parenthesis squared over denominator 2 end fraction plus straight c which is required solution. 

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

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