Solve the following differential equation for a general solu

Solve the following differential equation for a general solution. 2x + 3y + cos(y) = (xsin(y) - 3x)y\'

Solution

(2x + 3y + cos(y)) dx + (3x-xsin(y))dy = 0

M = (2x + 3y + cos(y))

N = (3x - xsin(y))

My = 3 - sin(y)

Nx = 3 - sin(y)

Hence the equation is exact

F = Integral ( Mdx) = x^2 + 3xy + xcos(y) + f(y)

F = Integral ( Ndy) = 3xy + xcos(y) + f(x)

Compairing the functions we get

x^2 + 3xy + xcos(y) = C as the funal solution of the differential equation