From the differential equation of the family of parabolas with focus at the origin and axis of symmetry along the x-axis. Find the order and degree of the differential equation.

Explanation

From the figure, equation of family of parabolas is
`y^(2)=4a(a+x)`……………(1)
Differentiating w.r.t. x, we get
`2y(dy)/(dx)=4a` or `y(dy)/(dx)=2a`…………….(2)
Eliminating a from (1) and (2), we get
`y^(2)=(y(dy)/(dx))^(2)+2y(dy)/(dx)x`
or `y^(2)=y^(2)((dy)/(dx))^(2)+2xy(dy)/(dx)`
Which has order 1 and degree 2.