Question: Constants in pdsolve


I need to solve below integro-differential equation

0.3846153846*(diff(F(x, y), y, y))+diff(F(x, y), x)-(diff(w(x), x, x))*y-(1/2)*(int(diff(F(x, y), x), y = -1 .. 1))+diff(F(x, y), x, x)-(diff(w(x), x, x, x))*y-(1/2)*(int(diff(F(x, y), x, x), y = -1 .. 1))

The solution is as follows:

(diff(w(x), x))*y-_C1*y/exp(x)-(1923076923/5000000000)*_c[2]*x*y+_C2*y+(1/6)*_c[2]*y^3+_C4*y+_F1(x)


The parameters _C1, _C2, c[2], C4 are functions of x, or functions of y? Or these parameters are constant numbers? 

In addition to, is it reasonable to use C *y instead of _C2*y+_C4*y ?


Thank you

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