Then, computing the resolvent amounts to solving the inhomogeneous equation, which can be done using the variation of parameters formula.
2.
Then any solution of the inhomogeneous equation may have a solution of the homogeneous equation added to it, and still remain a solution.
3.
A major obstacle was overcome when, in the 1990s, M . A . Golberg and C . S . Chen extended the MFS to deal with inhomogeneous equations and time-dependent problems.
4.
The difference space "'V "'is the kernel of, because the difference of two solutions of the inhomogeneous equation " c " } } lies in the kernel.
5.
For example in mathematical physics, the homogeneous equation may correspond to a physical theory formulated in empty space, while the inhomogeneous equation asks for more'realistic'solutions with some matter, or charged particles.
6.
While homogeneous equations are relatively easy to solve, this method allows the calculation of the coefficients of the general solution of the " in " homogeneous equation, and thus the complete general solution of the inhomogeneous equation can be determined.
7.
It is particularly important to the solution of the general case, since any complementary function can be added to a solution of the inhomogeneous equation to give another solution ( by a method traditionally called " particular integral and complementary function " ).
8.
:4 . " A FRW dark fluid with a non-linear inhomogeneous equation of state ", I Brevik, E Elizalde, O Gorbunova &-The European Physical Journal C, 2007-Springer http : / / www . springerlink . com / index / 94lp146483q306lg . pdf
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