A curve is such that $\dfrac{\mathrm{d}y}{\mathrm{d}x}=\dfrac{k}{\sqrt{2x+1}}$, where \(

Question

A curve is such that $\dfrac{\mathrm{d}y}{\mathrm{d}x}=\dfrac{k}{\sqrt{2x+1}}$, where $k$ is a constant. Given that the curve passes through the points $(0,4)$ and $(4,10)$, find the value of $k$ and the equation of the curve.[7]

Accepted Answer

$k=3,\quad y=3\sqrt{2x+1}+1$

Radical differential equation through two points

Radical differential equation through two points

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