I have the following ODE
c + (p + r) y[p] == p (u + (-1 + p) y'[p])
where car and u are parameters of the problem. I want to solve the ODE using a symbolic initial condition y(0)=x for some x, or also to impose an initial condition of the form y(z)=x where both x and y are symbols. For both these issues I tried to do DSolve, getting the solution with the constant C and then using Solve[y(0)==x, c] but I get error. I guess I should define a function y which maps p and c and use that in Solve. Is there any straightforward way to do this?