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Vector Algebra

Question
CBSEENMA12033014
Wired Faculty App

Solve the differential equation
left parenthesis tan squared straight x plus 2 space tanx space plus 5 right parenthesis space dy over dx space equals space 2 left parenthesis 1 plus tanx right parenthesis space sec squared straight x.

Solution
The given differential equation is
                open parentheses tan squared straight x plus 2 space tan space straight x plus 5 close parentheses space dy over dx space equals space 2 left parenthesis 1 minus tanx right parenthesis space sec squared straight x
or        dy over dx equals space fraction numerator 2 space sec squared straight x plus 2 space tanx space sec squared straight x over denominator tan squared straight x plus 2 space tanx plus 5 end fraction
Separating the variables,  we get,         
                      dy space equals space fraction numerator 2 space tanx space sec squared straight x space plus space 2 space sec squared straight x over denominator tan squared straight x plus 2 space tan space straight x plus 5 end fraction dx
Integrating ,   integral 1 space dy space equals space integral fraction numerator 2 space tanx space sec squared straight x space plus space 2 sec squared straight x over denominator tan squared straight x plus 2 space tan space straight x plus 5 end fraction dx
therefore space space space space space space space space space space space straight y equals log space open vertical bar tan squared straight x plus 2 tanx plus 5 close vertical bar space plus straight c space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space space integral fraction numerator straight f apostrophe left parenthesis straight x right parenthesis over denominator straight f left parenthesis straight x right parenthesis end fraction dx space equals space log space open vertical bar straight f left parenthesis straight x right parenthesis close vertical bar close square brackets
which is the 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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