A curve is such that $\dfrac{\mathrm{d}y}{\mathrm{d}x}=k\sin2x$, where $k$ is a consta

Question

A curve is such that $\dfrac{\mathrm{d}y}{\mathrm{d}x}=k\sin2x$, where $k$ is a constant. Given that the curve passes through the points $(0,1)$ and $\left(\dfrac{\pi}{4},5\right)$, find the value of $k$ and the equation of the curve.[7]

Accepted Answer

$k=8,\quad y=-4\cos2x+5$

Trigonometric differential equation through two points

Trigonometric differential equation through two points

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