Study GuideDifferential Equations–Applying Differential Equations1. Applications of First‐Order EquationsFirst-order differential equations show up in many real-world problems—from geometry and physics tochemistry and biology. In this chapter, we explore several important applications and learn how tomodel and solve them.1.1Orthogonal TrajectoriesWhat does “orthogonal” mean?•Orthogonalmeansperpendicular.•Atrajectoryis a path or curve.So,orthogonal trajectoriesare two families of curves that intersect each other at right angles (90°).1.2How do we know two curves are perpendicular?At any point where two curves intersect:•Their slopes must benegative reciprocalsof each other.•If one slope is(m), the other must be(-1/m).Since the slope of a curve is given by its derivative, two families of curvesare orthogonal wherever they intersect if:Example 1:Electric Field Lines and EquipotentialsPreview Mode
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