Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-1/13/c/ii/solution

The initial condition gives . Since belongs to the principal inverse sine range, choose in part (i). The particular solution is
The upper endpoint is excluded because there and the original tangent ceases to be defined.

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