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Solve the differential equation and determine the exact value of $y$ when $x=\sqrt{3}$.
Mathematics 9709 · AS & A Level · Differential equations
Differential equations — practice question
The variables $x$ and $y$ are linked by the differential equation $(x^2+1)\frac{dy}{dx}=kxe^{2y}$, where $k$ is a constant. It is also stated that $y=0$ when $x=0$ and that $y=-\frac{1}{2}$ when $x=1$.