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Solve the differential equation, and express $x^2$ in terms of $\theta$.
Mathematics 9709 · AS & A Level · Differential equations
Differential equations — practice question
The variables $x$ and $\theta$ are linked by the differential equation $\frac{x}{\tan \theta} \frac{dx}{d\theta} = x^2 + 3$. You are also told that $x = 1$ when $\theta = 0$.