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in Differential Equations by (35.1k points)
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The solution of the DE cos x (1 + cos y ) dx – sin y (1 + sin x) dy = 0 is

A. 1 + sin y cos y = C

B. (1 + sin y) (1 + cos y) = C

C. sin x cos y + cos y = C

D. none of these

1 Answer

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Best answer

Given cos x (1+cos y) dx – sin y (1+sin x) dy = 0

Let 1+cos y = t and 1+sin x = u

On differentiating both equations, we get

-sin y dy = dt and cos x dx = du

Substitute this in the first equation

t du + u dt = 0

-log u = log t + C

log u + log t = C

log ut = C

ut = C

(1+sin x)(1+cos y) = C

Conclusion: Therefore, (1+sin x)(1+cos y) = C is the solution of cos x (1+cos y) dx – sin y (1+sin x) dy = 0

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