A curve is such that $\dfrac{\mathrm{d}y}{\mathrm{d}x}=k\mathrm{e}^{2x}$, where $k$ is

Question

A curve is such that $\dfrac{\mathrm{d}y}{\mathrm{d}x}=k\mathrm{e}^{2x}$, where $k$ is a constant. Given that the curve passes through the points $(0,1)$ and $(\ln2,7)$, find the value of $k$ and the equation of the curve.[7]

Accepted Answer

$k=4,\quad y=2\mathrm e^{2x}-1$

Exponential differential equation through two points

Exponential differential equation through two points

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