求解微分方程y'*cos(y)=x+1-sin(y)

求解微分方程y'*cos(y)=x+1-sin(y)
求解微分方程y'*cos(y)=x+1-sin(y)

求解微分方程y'*cos(y)=x+1-sin(y)
y ' * cos(y) = x + 1 - sin(y) =>
y ' * cos(y) - 1 = x - sin(y) =>
(sin(y) - x) ' = x - sin(y) => 换元 sin(y) - x = t
t ' = dt / dx = -t =>
1/t dt = -1 dx 两边积分 => ln t = -x + C1 => t = C * e^(-x).
即 sin(y) - x = C * e^(-x) => sin(y) = C * e^(-x) + x =>
y = arcsin(C * e^(-x) + x).其中,C > 0为常数.