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henpen

  • 2 years ago

\[Ly=h(x)\] f is the linear combination of all the functions that are L(function)=0, so that \[Lf=0\] And g is ONE OF the functions that do this: \[Lg=h(x)\] Why is the general (i.e. total and only (minus degrees of freedom for unknowable coefficients)- is this the correct definition?) solution for y equal to this: \[y=f+g\] I understand that it WORKS, but I've read in many places to stop here, as I've found the 'general' solution (whatever that really means) despite only using 1 out of potentially many g that do this \[L(function)=h(x)\]? Does this rule only apply to a subset of differential equations, or are all other g not independent from out 1st g?

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