Exact Differential Equation and Orthogonal Trajectories

Exact differential equation || Orthogonal trajectory

Any curve which cuts every member of a given family of curve is called an orthogonal trajectory of family. To get this, we replace (dy)/(dx)by -(dx)/(dy) in differential equation. The orthogonal trajectories for y=ce^(-x) represent

Any curve which cuts every member of a given family of curve is called an orthogonal trajectory of family. To get this, we replace (dy)/(dx) by -(dx)/(dy) in differential equation. The orthogonal trajectories for y=cx^(2) , where c is a constant is

Exaction

Theory OF Exact Differential Equation and Some Basic Illustration

Illustration Based on Exact Differential Equation Mixture Problems and Orthogonal Trajectory

Find the orthogonal trajectories of xy=c

Find the orthogonal trajectories of xy=c

Theory OF Exact Differential Equation || Some Basic Illustration

Illustration Based on Exact Differential Equation Mixture Problems || Orthogonal Trajectory