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  4. The order and degree of differential equation of family of circles touching y axis at origin, is

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Q. The order and degree of differential equation of family of circles touching $y$ axis at origin, is

Differential Equations

Solution:

$ (x-\alpha)^2+(y-0)^2=\alpha^2$
$ x^2+y^2-2 \alpha x=0 ....$(i)
$ 2 x+2 y \frac{d y}{d x}-2 \alpha=0 $
$ \alpha=x+y \frac{d y}{d x} .....$(ii)
equation of differential equation
$ x^2+y^2=2 x\left(x+y \frac{d y}{d x}\right)$
order $=1$
degree $=1$