Question

Solve:
e^x tan y dx + (1 – e^x) sec² y dy = 0.

Solution

The given differential equation is
$straight e to the power of straight x space tany space dx space plus space left parenthesis 1 minus straight e to the power of straight x right parenthesis space sec squared straight y space dy space equals space 0$
or $left parenthesis 1 minus straight e to the power of straight x right parenthesis space sec squared straight y space dy space equals space minus straight e to the power of straight x space tan space straight y space dx space space space or space space space fraction numerator sec squared straight y over denominator tan space straight y end fraction space dy space equals space minus fraction numerator straight e to the power of straight x over denominator 1 minus straight e to the power of straight x end fraction dx$
$therefore space space space integral fraction numerator sec squared straight y over denominator tan space straight y end fraction dy space equals space integral fraction numerator negative straight e to the power of straight x over denominator 1 minus straight e to the power of straight x end fraction dx rightwards double arrow space space space space log space left parenthesis tan space straight y right parenthesis space equals space log space left parenthesis 1 minus straight e to the power of straight x right parenthesis space plus space log space straight e rightwards double arrow space space space space log space left parenthesis tan space straight y right parenthesis space equals space log space left square bracket straight e space left parenthesis 1 minus straight e to the power of straight x right parenthesis right square bracket therefore space space space space space space space tan space straight y space equals space straight e left parenthesis 1 minus straight e to the power of straight x right parenthesis space is space the space required space solution. space space$

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Vector Algebra

Solve:
e^x tan y dx + (1 – e^x) sec² y dy = 0.

Some More Questions From Vector Algebra Chapter

Determine order and degree (if defined) of differential equations:
y' + y = e^x

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Vector Algebra

Solve: ex tan y dx + (1 – ex) sec2 y dy = 0.

Some More Questions From Vector Algebra Chapter

Determine order and degree (if defined) of differential equations:y' + y = ex

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Solve:
e^x tan y dx + (1 – e^x) sec² y dy = 0.

Determine order and degree (if defined) of differential equations:
y' + y = e^x