# Solve the Differential Equation : X D Y D X + Y − X + Xy Cot X = 0 ; X ≠ 0 . - Mathematics

Sum

Solve the differential equation : "x"(d"y")/(d"x") + "y" - "x" + "xy"cot"x" = 0; "x" != 0.

#### Solution

x dy/dx + y - x + xy cos x = 0

⇒ dy/dx + (1/x + cot x ) y = 1

I.F. = e^(int(1/x + cot x) dx) = e^(log(x sin x))

= x sin x

∴ y xx  x sin x = x sinx dx

⇒ xy sin x = - x cos x + sin x + C

Concept: Solutions of Linear Differential Equation
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