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Solve the differential equation and express $x$ in terms of $\cos \theta$.
Mathematics 9709 · AS & A Level · Differential equations
Differential equations — practice question
The variables $x$ and $\theta$ are linked by the differential equation $\sin \frac{1}{2}\theta\, \frac{dx}{d\theta} = (x + 2)\cos \frac{1}{2}\theta$ for $0 < \theta < \pi$. It is given that $x = 1$ when $\theta = \frac{1}{3}\pi$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “By separating variables, get $\int\frac1{x+2}\,dx=\int\cot\frac12\theta\,d\theta$” …
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