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