Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of x-axis.

Explanation

Equation of parabola having vertex at origin and axis along the positive direction of x-axis is


`y^{2}=4 ax`


Differentiating both sides of equation,


`2 y frac{d y}{d x}=4 a`


`Rightarrow a=y fracy2 fracdyd x`


Put the value of a in `y^2=4 ax`


`y^{2}=4(y frac{y}{2} frac{dy}{dx}) {x}`


`Rightarrow y=2 x frac{dy}{dx} `


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