Question

Solve the following exact differential equation. You don't have to show that it is exact. (ecos(y) - esin(x)) + (esin(x) - e* sin(y)]y' = 0 Solution.

Answer 1

There is a printing mistake in the in the question. Let's If Then see how ? we consider that your question is right e cos (Y) – er Sin (²) er sin (x) ay M= ӘМ e sin (y) – en and Z x Sin (②) esin () ON e Cosa x e Sin (y) am ƏN The given tax exact. is exaer. differential equation is not But it is given that the differential equation There fore, the have a question printing mistake. exact equation will * Cos () – e Sin (x)) + e Sin (y The be , 0 e Cos et sin (a) con e Porte) - e" su cu) by =0

In this case, x M = Sin ) am - ay e Cos (Y) * Esin (%)) - et sin (4) Sin (2) (y) – er sin(x). ОМ ay and N = 2 e Cos Sin (4) ON ( Sinks) eě Sin (Y) 4 AN dx 1 sin (x) e Sin (9) ON x é sin) dx Sin (x (X) aN 2x .. ам The ay Solution of the Problem : equation ition i exact. 7 《一 a e Ces (4) – e sin e since) d = (étanto) – e suce) esco leto Le si e Sin (1) dy et cos @) dy – é sin(x) da 3 d (e*@y) + d(e cosz) = los (Y) de + =0 = 0

both sides, =C Integrate Sale Cosy) + S«Cetcos) > e Cosy ter cosa=e This & the required solution .
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