using an integrating factor, find the general solution of the differential equation dy/dx +y(tanx)=tan^3(x)sec(x)

This is a first order differential equation, but initially it is not solvable as both the X&Y's can't be separated from eachother directly. An integrating factor is a specific value that when multiplied can render the equation integratable on the left side. Firstly dy/dx +yp(x)=q(x) is the traditional form of this type of differential equation, and how we find the integrating factor is by calculating IF=e^int(px)dx (int=integrate) .So by integating tan(x) we get ln|sec(x)|, thus e^{ln|sec(x)|​}=sec(x). Apply this to the intial equation by multiplying each side by sec(x), which equals  sec(x)dy/dx+ytan(x)sec(x)=tan³(x)sec²(x), d/dx[ysec(x)]=tan³(x)sec²(x), ysec(x)=int(tan³(x)sec²(x)dx) Integrating by substitution: let y=tan(x), dy/dx=sec²(x), thus ysec(x)=int(y³dy)=y⁴/4+c=tan⁴(x)/4+c Therefore the general solution to the differential equation is: y=cos(x)tan⁴(x)/4+c(cos(x))=sin(x)tan³(x)/4+c(cos(x)). Where c(cos(x)) is a constant