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In this problem we consider an equation in differential form M dx + N dy =...

Question:

In this problem we consider an equation in differential form M dx + N dy = 0. The equation (2е — (16х° уе* + 4e * sin(x))) d

In this problem we consider an equation in differential form M dx + N dy = 0. The equation (2е' — (16х° уе* + 4e * sin(x))) dx + (2eY — 16х*y'е*)dy 3D 0 in differential form M dx + N dy = 0 is not exact. Indeed, we have For this exercise we can find an integrating factor which is a function of x alone since м.- N. N can be considered as a function of x alone. Namely we have u(x) = Multiplying the original equation by the integrating factor we obtain a new equation M dx + N dy = 0 where M = N = Which is exact since м, = N = are equal. This problem is exact. Therefore an implicit general solution can be written in the form F(x, y) = C where F(x, у) %3

Answers

Soluhon we au giren to solve the olon difforental eauction (a (16x e-e* sinn)). - 16fe-)dy form 4 3 Jhe abore ariation an beNO w, Ret-16e ae-16xe NQ | = J), q tunchion alon NOW Si-du imtegrahing facton, the Muttiplying equalion we have eaei6yee^simnThus, th tquwd soluhon i C. Termu ea from Jaey-164sim) de ae edr -16 xdu -4 sim du odyec = C 4 cas uty -yuy tч su c e whre C,

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