help on the last part.

In this problem we consider an equation in differential form M de | Ndy = 0. The equation (Belly - (12?g'e " ( de sin(a)) ) da | (93x - 12, ye * )dy =0 in differential form M da: | N dy - 0 is not exact Indeed, we have M . - N . Se (3y)-1200-xy"2x*3 For this exercise we can find an integrating factor which is a function of & alone since My N .. N can be considered as a function of a alone. Namely we have ur(x) = ex Multiplying the original equation by the integrating factor we obtain a new equation M da: { Ndy : 0 where M = (3e(3y)0/x-(12x*2y*3+4sin(x))) N - (9e*(3yje*x-12x*3y*2) Which is exact since Miser (3yle^[x)-36x"2y"2) are equal This problem is exact. Therefore an implicit general solution can be written in the form F(x, y) - C where F(, /) - -By 3x*3-4cos(x)+be"(3y+x)