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Vector Algebra

Question
CBSEENMA12033049
Wired Faculty App

For the following differential equation, find the general solution:
sec2 x tan y dx – sec2 y tan x dy = 0.

Solution
The given differential equation is
                sec2 x tan y dx – sec2 y tan x dy = 0.
or    sec2 x tan y dx = sec2y tan x dy 
or     fraction numerator sec squared straight y over denominator tan space straight y end fraction dy space equals space fraction numerator sec squared straight x over denominator tan space straight x end fraction dx
Integrating,  we get,
                integral fraction numerator sec squared straight y over denominator tan space straight y end fraction dy space equals space integral fraction numerator sec squared straight x over denominator tanx end fraction dx
or      log space open vertical bar tan space space straight y close vertical bar space equals space log space open vertical bar space tan space straight x close vertical bar space plus space log space straight A
or space space log space open vertical bar tan space straight y close vertical bar space minus space log space open vertical bar tan space straight x close vertical bar space equals space log space straight A or space space log space open parentheses fraction numerator open vertical bar tan space straight y close vertical bar over denominator open vertical bar tan space straight x close vertical bar end fraction close parentheses space equals space log space space straight A space space space space space space space space space space space space space space space space space space space space space space space space or space space space log space open vertical bar fraction numerator tan space straight y over denominator tan space straight x end fraction close vertical bar space equals space log space straight A or space space space space space space space space space space open vertical bar fraction numerator tan space straight y over denominator tan space straight x end fraction close vertical bar space equals straight A 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 space space space space space space space space space or space space space space fraction numerator tan space straight y over denominator tan space straight x end fraction space equals space plus-or-minus space straight A or space space space space space fraction numerator tan space straight y over denominator tan space straight x end fraction space equals straight c comma space space space where space straight c space is space arbitrary space constant. space or space space space space space tan space straight y space equals space straight c space tanx space comma space which space is space required space solution. space

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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