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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8

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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