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.

Question

Philoid · Accepted Answer

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