Find initial value of differential equation

Question

Solve the initial-value problem that consists of the differential equation

sec x dy + csc y dx = 0 and the initial condition y(1)= π/2

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Answer 1

We separate variables and integrate - ∫sinydy = ∫cosxdx; cosy = sinx + C; cos(π/2) = sin1 + C; C = - sin1;

cosy = sinx - sin1.