一阶线性微分方程 y′+P(x)y=Q(x)y'+P(x)y=Q(x)y′+P(x)y=Q(x) 的通解公式:
y=Ce−∫P(x) dx+e−∫P(x) dx∫Q(x)e∫P(x) dx dxy=Ce^{ -\int P(x) \, dx }+e^{ -\int P(x) \, dx }\int Q(x)e^{ \int P(x) \, dx } \, dx y=Ce−∫P(x)dx+e−∫P(x)dx∫Q(x)e∫P(x)dxdx