PROBLEM: Verify that the functions [x+1]e^(-t) ; e^(-2)sint ; and xt are respectively solutions of the nonhomogeneous equations(adsbygoogle = window.adsbygoogle || []).push({});

Hu = -e^(-t)[x+1] ; Hu = e^(-2x)[4sint+cost] ; and Hu = x

where H is the 1D heat operator H = [tex]\frac{\partial}{\partial t}[/tex] - [tex]\frac{\partial^2}{\partial x^2}[/tex]

i did this the verification part,, the problem is with the second part of the problem

Find a solution of the PDE

Hu = [tex]\sqrt{2} x[/tex] + [Pi]e^(-2x) [4sint + cost] + e^(-t)[x+1]

isn't the first part a solution for this PDE? i dont understand the question

any hints how to setup this PDE?

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# Verifying if this PDE is a solution

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