First off I am NOT asking you to solve this for me. I'm just trying to understand the concept behind this problem.(adsbygoogle = window.adsbygoogle || []).push({});

Let L be a linear transformation defined by

L[p]=(x^2+2)p"+ (x-1)p' -4p

I have not seen linear transformations in this format. Usually I see something like L(x)=x1b1+ x2b2.. and they usually give me a basis at least. There's something that I am not seeing here and I would appreciate a nudge in the right direction

i've looked through several books and have not found a linear transformation of this type. if you know of an online resource or a book that covers this please do let me know

thanks

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# Linear transformation of a 2nd order pde

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