2016-2015Babylon University First Course Ordinary Differential Equations

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2016-2015Babylon University First Course Ordinary Differential Equations

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Such orthognal systems of curves are particulare importance in physical problems related to

electrical potential (flow of electric current and other to curves of constant potential ) , they also

occure in hydrodynamics and heat flow problems .

Figure (1)An orthogonal trajectory intersects the family of curves at right angles ,

2016-2015Babylon University First Course Ordinary Differential Equations

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Figure (2)Every stright line through the origion is

Every stright line through the origion is

Orthognonal to the family of circals centered at the origion

2016-2015Babylon University First Course Ordinary Differential Equations

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Figure ( 3 )

2016-2015Babylon University First Course Ordinary Differential Equations

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Figure(4)

2016-2015Babylon University First Course Ordinary Differential Equations

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2016-2015Babylon University First Course Ordinary Differential Equations

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Figure(5)

2016-2015Babylon University First Course Ordinary Differential Equations

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Figure(6)

2016-2015Babylon University First Course Ordinary Differential Equations

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2016-2015Babylon University First Course Ordinary Differential Equations

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Figure (7)

2016-2015Babylon University First Course Ordinary Differential Equations

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2016-2015Babylon University First Course Ordinary Differential Equations

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1. Find the orthognal trajectories of the family of curves

2. Find the orthognal trajectories of the family of circuls