求解微分方程dy/dx=y^2cosx 满足初值条件y(0)=1的解

这是分离变量的方程：dy/dx = y^2 * cosx =>1 / y^2 dy = cos x dx 积分=>-1/y = sin x + C =>y = -1 / (sin x + C).y(0) = 1 代入 => C = -1.故 y = -1 / (sin x - 1) = 1 / (1 - sin x).