The general solution of x d y d x = y - x tan ⁡ y x is ________

Question

The general solution of x d y d x = y - x tan ⁡ y x is ________, x 2 sin ⁡ x y = c, x sin ⁡ x y = c, x sin ⁡ y x = c, x 2 sin ⁡ y x = c

MARKS App · Accepted Answer

Given equation is d y d x = y x - t a n y x is Homogeneous equation, then Put y = v x and d y d x = v + x d v d x Then, v + x d v d x = v - t a n v ⇒ d v t a n v = - d x x (integrate both sides) ln ⁡ sin ⁡ v = – ln ⁡ x + ln ⁡ c l n x ⋅ s i n y x = ln ⁡ c ⇒ x s i n y x = c

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