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Given family of curves: $$F(x,y,c)=0$$.
Differential equation: $$\frac{dy}{dx} = f(x,y)$$.
Orthogonal trajectories: Replace $$\frac{dy}{dx}$$ with $$-\frac{dx}{dy}$$ and solve $$-\frac{dx}{dy} = f(x,y)$$.
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