Solve:
3e^x tan y dx + (1 – e^x) sec²y dy = 0.

Solution

The given differential equation is
3e^x tan y dx + (1 – e^x) sec²y dy = 0
or $left parenthesis 1 minus straight e to the power of straight x right parenthesis space sec squared straight y space dy space equals negative 3 space straight e to the power of straight x space tan space straight y space dx space space space or space space space fraction numerator sec squared straight y over denominator tan space straight y end fraction dy space equals space minus 3 fraction numerator straight e to the power of straight x over denominator 1 minus straight e to the power of straight x end fraction dx$
$therefore space space space space integral fraction numerator sec squared straight y over denominator tan space straight y end fraction dy space equals 3 integral fraction numerator straight e to the power of negative straight x end exponent over denominator 1 minus straight e to the power of straight x end fraction dx space space space space space space space rightwards double arrow space space space space log space left parenthesis tan space straight y right parenthesis space equals space 3 space log space left parenthesis 1 minus straight e to the power of straight x right parenthesis space plus space log space straight c$
$therefore space space space log space left parenthesis tan space straight y right parenthesis space equals space log space left parenthesis 1 minus straight e to the power of straight x right parenthesis cubed plus space log space straight c space space space space rightwards double arrow space space space log space left parenthesis tany right parenthesis space equals space log space open square brackets straight e left parenthesis 1 minus straight e to the power of straight x right parenthesis cubed close square brackets therefore space space space tan space straight y space equals space straight e left parenthesis 1 minus straight e to the power of straight x right parenthesis cubed space is space the space required space solution. space$

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Vector Algebra

Solve:
3e^x tan y dx + (1 – e^x) sec²y dy = 0.

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Vector Algebra

Solve:3ex tan y dx + (1 – ex) sec2y dy = 0.

Some More Questions From Vector Algebra Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Solve:
3e^x tan y dx + (1 – e^x) sec²y dy = 0.