Question

The equation of the curve passing through the point `(0, pi/4)` whose differential equation is sin x cos y dx + cos x sin y dy = 0, is

पर्याय

• sec x sec y = `sqrt(2)`

• cos x cos y = `sqrt(y)`

• sec x = `sqrt(2)` cos y

• cos y = `sqrt(2)` sec y

Answer 1

sec x sec y = `sqrt(2)`

Explanation:

The given differential equation is sin x cos y dx + cos x sin y dy = 0

Dividing by cos x cos y ⇒ `sin x/cos x dx + sin y/cos y dy` = 0

Integrating, `int tan x  dx + int tan y  dy` = log c

or log sec x sec y = log c or sec x sec y = c

Curve passes through the point `(0, pi/4)`

`sec 0 sec  pi/4 = c = sqrt(2)`

Hence, the required eqution of the curve is sec x sec y = `sqrt(2)`