Mathematics Part-II

Book: Mathematics Part-II

Chapter: 9. Differential Equations

Subject: Maths - Class 12th

Q. No. 8 of Miscellaneous Exercise

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Find the equation of the curve passing through the point whose differential equation is sin x cos y dx + cos x sin y dy = 0.

It is given that sin x cos y dx + cos x sin y dy = 0

tanxdx + tanydy = 0

So, on integrating both sides, we get,

log(secx) + log(secy) = logC

log(secx.secy) = log C

secx.secy = C

The curve passes through point

Thus, 1× = C

C =

On substituting C = in equation (1), we get,

secx.secy =

Therefore, the required equation of the curve is


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