Simple ODE question

[sozo91]

How do I find the oblique trajectories to the following family of curves:

y = x-1 + c*e^-x

[arunbg]

First find the differential equation to the family of curves given by differentiation wrt x and eliminating c. dy/dx will give slope of the curves at any point. If another curve's tangent makes an angle 'A', with this curve whose tangent at point of intersection is at an angle 'B', using tan formula:
tan(A+B)= (tanA+tanB)/(1-tanAtanB)

What are tanA and tanB to be substituted with next?