It applies the DSolve function to dissolve the equation and separate into terms of y[x] and x alone.

DSolve tests if the sum y’[x] + y[x] is equal to a*Sin[x] and returns y[x] if so or x if not.

It solves a first order differential equation for the function y[x] but no boundary condition has yet been specified.

It solves a first order differential equation in y[x] using the boundary condition mySolve = a*Sin[x]