Mathematics, 22.09.2019 05:10 sanociahnoel
Find linearly independent functions that are annihilated by the given differential operator. (give as many functions as possible. use x as the independent variable. enter your answers as a comma-separated list.) d2 − 12d − 45
Answers: 1
such that![(D^2-12D-45)[f(x)]=0](/tpl/images/0251/2663/2f3b0.png)
![(D^2-12D-45)[f]=(D-15)(D+3)[f]=0](/tpl/images/0251/2663/c0854.png)
![(D-15)[f]=0\implies f'-15f=0\implies f(x)=e^{15x}](/tpl/images/0251/2663/d43ba.png)
![(D+3)[f]=0\implies f'+3f=0\implies f(x)=e^{-3x}](/tpl/images/0251/2663/1f441.png)
![(D^2-12D-45)[e^{15x}]=225e^{15x}-12(15e^{15x})-45e^{15x}=0](/tpl/images/0251/2663/d3a4f.png)
![(D^2-12D-45)[e^{-3x}]=9e^{-3x}-12(-3e^{-3x})-45e^{-3x}=0](/tpl/images/0251/2663/01b7a.png)
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