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This is typically the first solver to try on a new problem. Ode23s is suitable for stiff problem where lower accuracy is acceptable. Example 6.1: Write the well-known van der pol equation  EMBED Equation.3  into a system of ODE. Let  EMBED Equation.3 ,  EMBED Equation.3 . Then  EMBED Equation.3   EMBED Equation.3 . In the following we show how to use the Matlab ODE solvers and sketch the graph. Example 6.2: Use ode45 solver to solve  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3  clear all format long global  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  input(Please input  EMBED Equation.3 );  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 ; [t y]=ode45(test1, [t0 tf],y0); plot EMBED Equation.3   EMBED Equation.3 label EMBED Equation.3 ;  EMBED Equation.3 label EMBED Equation.3 ; Xmin=0; Xmax=85; Ymin=0; Ymax=16; axis([Xmin,Xmax,Ymin,Ymax]); disp(finish) function dy=test1(t,y) global  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 ;  Example 6.3: Solve the Van der Pol equation  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 . function  EMBED Equation.3 =vdpol( EMBED Equation.3 , EMBED Equation.3 ) %VDPOL van der Pol equation. %  EMBED Equation.3 =VDPOL( EMBED Equation.3 , EMBED Equation.3 ) %  EMBED Equation.3  %  EMBED Equation.3  %  EMBED Equation.3   EMBED Equation.3 ;  EMBED Equation.3 ; Note that the input arguments are  EMBED Equation.3  and  EMBED Equation.3  but that the function does not use  EMBED Equation.3 . Note also that the output  EMBED Equation.3  must be a column vector. 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