Find y if dy/dx = y² sec²(x), given that y(0) = 1

1/y² dy/dx = sec²(x)∫ 1/y² dy/dx dx = ∫ sec²(x) dx-1/y + C₁ = tan(x) + C₂y = -1/(tan(x) + A) where A = C₂ - C₁y(0) = -1/A so y(0) = 1 means A = -1. Finished!