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  4. The differential equation of all parabolas whose axis of symmetry is along axis of x-axis is of order

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Q. The differential equation of all parabolas whose axis of symmetry is along axis of $x$-axis is of order

Differential Equations

Solution:

The general form of the equation of parabola whose symmetry is along $x$-axis is given by $x = ay^2 + b$, which is the solution of the differential equation of all such type of parabola which contains two arbitrary constant so the order of differential equation is $2$.