I'm not quite sure if this is a linear functional but the question asks:(adsbygoogle = window.adsbygoogle || []).push({});

if [tex]L=D^2+4xD-2x[/tex] and [tex]y(x)=2x-4e^{5x}[/tex]

I am to find Ly=?

My first impressions to solve this is the take [tex]Ly=y''(x)+4xy'(x)-2x[/tex]

i'm not quite sure how to solve this but I got:

[tex]y''(x)=-100e^{5x}[/tex]

[tex]y'(x)=-20e^{5x}+2[/tex]

and then I plug it into [tex]Ly=y''(x)+4xy'(x)-2x[/tex]

I dont think I did this correctly, could someone help me out?

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# Linear functionals?

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