定数変化法
A = A(x), B = B(x) は
A ′ ( x ) u 1 ( x ) + B ′ ( x ) u 2 ( x ) = 0 {\displaystyle A'(x)u_{1}(x)+B'(x)u_{2}(x)=0}
となるものと仮定すると、
u G ′ ( x ) = A ( x ) u 1 ′ ( x ) + B ( x ) u 2 ′ ( x ) {\displaystyle u_{G}'(x)=A(x)u_{1}'(x)+B(x)u_{2}'(x)}
となり、さらに微分して
u G ′′ ( x ) = A ( x ) u 1 ′′ ( x ) + B ( x ) u 2 ′′ ( x ) + A ′ ( x ) u 1 ′ ( x ) + B ′ ( x ) u 2 ′ ( x ) {\displaystyle u_{G}''(x)=A(x)u_{1}''(x)+B(x)u_{2}''(x)+A'(x)u_{1}'(x)+B'(x)u_{2}'(x)}
を得る。従って、L の uG への作用は
L u G = A ( x ) L u 1 ( x ) + B ( x ) L u 2 ( x ) + A ′ ( x ) u 1 ′ ( x ) + B ′ ( x ) u 2 ′ ( x ) {\displaystyle Lu_{G}=A(x)Lu_{1}(x)+B(x)Lu_{2}(x)+A'(x)u_{1}'(x)+B'(x)u_{2}'(x)}