Continuous dynamic systems39Furthermore, if we have the initial condition thaty(0)=y0, then we cansolve forcy0=−ab+cc=y0+abHence, we have the solution to the initial value problem ofy(t)ab+±y0+ab²ebtExample 2.11Suppose we have the initial value problemdydt=2y+4ty(0)=1Applying the four-step procedure we haveStep 1−2y=4tStep 2µ(t)=e³−2=e−2tStep 3e−2ty=´4te−2t+cStep 4e−2ty2te−2t−e−2t+cOry2t−1+ce2tSincey(0)=1, then11+cc=2Hence,y(t)2t−1+2e2t2.3 Compound interestIf an amountAis compounded annually at a market interest rate of
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This note was uploaded on 12/14/2011 for the course ECO 3023 taught by Professor Dr.gwartney during the Fall '11 term at FSU.