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Find the solution to the differential equation and determine the value of $x$ when $\theta = \frac{\pi}{4}$, giving your answer correct to $3$ significant figures.
Mathematics 9709 · AS & A Level · Differential equations
Differential equations — practice question
The variables $x$ and $\theta$ are related by the differential equation $\frac{dx}{d\theta} = (x + 2) \sin^2 2\theta$, and the condition $x = 0$ applies when $\theta = 0$.