Variation of parameters: Difference between revisions

Revision as of 11:29, 11 September 2019

Revision as of 11:31, 11 September 2019

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as required.

The general method of variation of parameters allows for solution ofsolving an inhomogeneous linear equation

:<math>Lx(t)=F(t)</math>

by interpretingmeans of considering the second-order linear differential operator ''L'' asto be the net force, so thatthus the total impulse imparted to a solution between time ''s'' and ''s''+''ds'' is ''F''(''s'')''ds''. Denote by <math>x_s </math> the solution of the homogeneous initial value problem

:<math>Lx(t)=0, \quad x(s)=0, x'(s)=F (s)\,ds. </math>

Then a particular solution of the inhomogeneous equation is