Question

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

Answer 1

= J), q tunchion alon NOW Si-du imtegrahing facton, the Muttiplying equalion we have eaei6yee^simnfetu + e* &e* -16w?e)dy 3 4 Whera M d (aett16xsinm) - 64x We e a nd Jhui imklu that equation Tharefora (s exqd \r\nThus, th tquwd soluhon i C. Termu ea from Jaey-164sim) de ae edr -16 xdu -4 sim du odyec = C 4 cas uty -yuy t? su c e whre C, is the ons tant C X "",""error"":null,""modified"":1560766432,""source"":""automated""}"