Given y'[x]+3 Sin[x]-3-Cos[x]-2 y[x]==0 how to rewrite it to be y'[x]==3+Cos[x]-3 Sin[x]+2 y[x] i.e. put y'[x] on one side, and the rest on the other side?
ClearAll[f,x,y] expr=y'[x]+3 Sin[x]-3-Cos[x]-2 y[x]==0; lhs=expr/.lhs_==rhs_:>lhs; rhs=expr/.lhs_==rhs_:>rhs; rhs=-(lhs/.(y'[x]+any_.):>any)+rhs; expr=y'[x]==rhs
This makes it easier to make it in form \(y'(x)=f(x,y)\).