Systems of first-order differential equations185Hence,x1=x0+f(x0,y0)t=2+3(0.01)=2.03y1=y0+g(x0,y0)t=2+3(0.01)=2.03andf(x1,y1)= −2(2.03)−2.03+9=2.91g(x1,y1)= −2.03+2.03+3=3givingx2=x1+f(x1,y1)t=2.03+2.91(0.01)=2.0591y2=y1+g(x1,y1)t=2.03+3(0.01)=2.06This process is repeated. But all this can readily be set out on a spreadsheet, asshown in figure 4.33.The first two columns are simply the differential equations. Columns (3) and(4) employ the Euler approximation using relative addresses and the absoluteaddress fort. Thex-yplot gives the trajectory of the system in the phaseplane, with initial value (
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