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  4. The differential equation of all circles in the first quadrant which touch the coordinate axes is of order

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Q. The differential equation of all circles in the first quadrant which touch the coordinate axes is of order

Differential Equations

Solution:

The equation of the family of circles which touch both the axes is $(x - a)^2 + (y - a)^2 = a^2$, where $a$ is a parameter. This is one parameter family of curve. So its differential equation is of order one.