Hill differential equation

In mathematics, the Hill equation or Hill differential equation is the second-order linear ordinary differential equation d 2 y d t 2 + f ( t ) y = 0 , {\displaystyle {\frac {d^{2}y}{dt^{2}}}+f(t)y=0,} where f ( t ) {\displaystyle f(t)} is a periodic function with minimal period π {\displaystyle \pi } . By this we mean that for all t {\displaystyle t} f ( t + π ) = f ( t ) , {\displaystyle f(t+\pi )=f(t),} and if p {\displaystyle p} is a number with 0 < p < π {\displaystyle 0<p<\pi } , the equation f ( t + p ) = f ( t ) {\displaystyle f(t+p)=f(t)} must fail for some t {\displaystyle t} .

Source: Wikipedia — Hill differential equation (CC BY-SA 4.0)

Hill differential equation

In mathematics, the Hill equation or Hill differential equation is the second-order linear ordinary differential equation d 2 y d t 2 + f ( t ) y = 0 , {\displaystyle {\frac {d^{2}y}{dt^{2}}}+f(t)y=0,} where f ( t ) {\displaystyle f(t)} is a periodic function with minimal period π {\displaystyle \pi } . By this we mean that for all t {\displaystyle t} f ( t + π ) = f ( t ) , {\displaystyle f(t+\pi )=f(t),} and if p {\displaystyle p} is a number with 0 < p < π {\displaystyle 0<p<\pi } , the equation f ( t + p ) = f ( t ) {\displaystyle f(t+p)=f(t)} must fail for some t {\displaystyle t} .

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Source: Wikipedia "Hill differential equation" · CC BY-SA 4.0

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