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henpen
 3 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?
henpen
 3 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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