高等数学题:设f(x,y)=e^(cx)g(y)满足方程fx+fy=o,则g(y)=

fx = c * e^(cx) * g(y),fy = e^(cx) * g ' (y),fx + fy = 0 => c * e^(cx) * g(y) + e^(cx) * g ' (y) = 0
=> g ' (y) + c * g(y) = 0 => dg(y) / dy + c * g(y) = 0,分离变量法 =>
1 / g(y) dg(y) = -c dy 积分=> ln g(y) = -cy + C1 => g(y) = C2 * e^(-cy),其中 C2 > 0 为常数.