Finding Oblique Trajectories to y=x-1+c*e^-x

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

y = x-1 + c*e^-x
 
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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?
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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