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The differential equation of all parabol...

The differential equation of all parabolas whose axis are parallel to the y-axis is

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Parabola having axis parallel to y-axis, represent the quadratic function,
`y=ax^(2)+bx+c` …………….(1)
Here, we have three effective constants: a,b and c.
`y^(')=2ax+b`
`y^('')=2a`
and `y^('')=0`, which is required differential equation.
Order of differential equation is three.
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