Solve the given differential equation sin yx xy y x cosyxS

Solve the given differential equation sin (y/x) (xy\' - y) = x cos(y/x).

Solution

given differential equation sin(y/x)(xy\'-y)=xcos(y/x)

which can be written as sin(y/x)(xdy/dx-y) = x cos(y/x)

we know that sin(y/x)/cos(y/x) =tan(y/x)

tan(y/x) (x dy/dx - y) = x

tan(y/x).x.dy/dx - tan(y/x) y =x

tan(y/x).x.dy/dx = x + tan(y/x) y

dy/dx = x + tan(y/x) y / (tan(y/x).x

which is seperable , not - linear and not-exact equation