Consider the family of curves y = kx2, where k is a constant. (a) Show that the differential equation of the family of orthogonal trajectories is dy/dx = − x/2y . (b) On the same axes sketch the slope field for the preceding differential equation and several members of the given family of curves. Describe the family of orthogonal trajectories.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.