Orthogonal trajectories are a family of curves (say \(F_2\)) in a plane that intersect a given family of curves (say \(F_1\)) at right angles.

Suppose \(F_1\) is given by \[y=c e^{-x^2}\] where \(y=y(x)\) and \(c\) is an arbitrary constant. Derive an equation for \(F_2\) where \(c\) is an arbitrary constant of integration.

**Hint:** If \(F_1\) is defined by a differential equation of the form \(y'=f(x,y)\), then \(F_2\) is defined by the differential equation \(y'=-\frac{1}{f(x,y)}\) (*why?*).

×

Problem Loading...

Note Loading...

Set Loading...