# Question:Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

## Question:Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

Maple 2018
 > restart:
 > Digits:= trunc(evalhf(Digits)); #generally a very efficient setting
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Setup of BVP system:

 > #ordinary differential equations: ODEs:= [    #Eq 1:    A1*(diff(f(x), x, x, x))/(A2*phi)-(diff(f(x), x))^2-M^2*(f(x))+f(x)*(diff(f(x), x, x)),    #Eq 2:    A4*Pr*phi*(diff(Theta(x), x, x))/A3+f(x)*(diff(Theta(x), x))+Q*Theta(x)        #All these ODEs are implicitly equated to 0. ]: ; #Display the ODEs.
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 > #parameter values that remain fixed for the entire set of plots: Pc:= phi=0.05:
 > #parameter values that remain fixed with each of the four plots:: Ps:= [    [fw=0.2, Pr=6.2, M=0.5],    [fw=0.2, Q=0.3, M=0.5],    [fw=0.2, Pr=6.2, Q=0.3],    [Q=0.3, Pr=6.2, M=0.5] ]: #parameter value for each curve Pv:= [    Q=[0.2, 0.4, 0.6, 0.8],    Pr=[0.7, 1.4, 2.1, 2.8],    M=[0.6, 1.2, 1.8, 2.4],    fw=[1, 2, 3, 4] ]:
 > for i to nops(Ps) do    plots:-display(       [seq(          plots:-odeplot(             Solve(lhs(Pv[i])= rhs(Pv[i])[j], Ps[i][], Pc),             [x, Theta(x)], 'color'= colseq[j], 'legend'= [lhs(Pv[i])= rhs(Pv[i])[j]]          ),          j= 1..nops(rhs(Pv[i]))       )],       'axes'= 'boxed', 'gridlines'= false,       'labelfont'= ['TIMES', 'BOLDOBLIQUE', 16],       'caption'= nprintf(          cat("\n%a = %4.2f, "\$nops(Ps[i])-1, "%a = %4.2f\n\n"), (lhs,rhs)~(Ps[i])[]       ),       'captionfont'= ['TIMES', 16]    ) od;
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 > #procedure that extracts Nusselt number from dsolve solution: GetNu:= (Sol::Matrix)-> Sol[2,1][1, Solve:-Pos(:-Nu)]:
 > Q:= [0.2, 0.4, 0.6]: plots:-display(    [seq(       ParamPlot2d(          GetNu, fw= 1..4, [M= 0.5],          'dsolveopts'= [Q= Q[k], Pr=6.2,  phi=0.05],          'legend'= [Q= Q[k]], 'color'= colseq[k], 'labels'= [fw, Nu]       ),       k= 1..nops(Q)    )] );
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