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Find the solution of the differential equation, writing $y$ as a function of $x$.
Mathematics 9709 · AS & A Level · Differential equations
Differential equations — practice question
The variables $x$ and $y$ are related by the differential equation $\frac{dy}{dx} = ky^3 e^{-x}$, where $k$ is a constant. It is known that $y = 1$ when $x = 0$, and that $y = \sqrt{e}$ when $x = 1$.
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