Determination of the series c_i. An equation with one catalytic variable and 2 additional unknown series Q'(0) and Q'''(0)
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> | factor(series(normal(eqinv),y,1)); |
> | c4sol:=factor(solve(coeff(%,y,-8),c[4])); |
> | factor(series(subs(c[4]=c4sol,normal(eqinv)),y,3)); |
> | c3sol:=factor(solve(coeff(%,y,-6),c[3])); |
> | factor(series(subs(c[4]=c4sol,c[3]=c3sol,normal(eqinv)),y,5)); |
> | c2sol:=collect(solve(coeff(%,y,-4),c[2]),t,factor); |
> | factor(series(subs(c[4]=c4sol,c[3]=c3sol,c[2]=c2sol,normal(eqinv)),y,6)); |
> | factor(subs(Q(0)=1,series(subs(c[4]=c4sol,c[3]=c3sol,c[2]=c2sol,normal(eqinv)),y,7))); |
> | c1sol:=collect(solve(coeff(%,y,-2),c[1]),[Q,t],factor); |
> | res:=subs(Q(0)=1,factor(series(subs(c[4]=c4sol,c[3]=c3sol,c[2]=c2sol,c[1]=c1sol,normal(eqinv)),y,9))); |
> | D2Qsol:=factor(solve(coeff(res,y,-1),`@@`(D,2)(Q)(0))); |
> | c0sol:=collect(solve(subs(`@@`(D,2)(Q)(0)=D2Qsol,coeff(res,y,0)),c[0]),[Q,t],factor); |
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The equation with one catalytic variable in Q(y)
> | factor(subs(c[4]=c4sol,c[3]=c3sol,c[2]=c2sol,c[1]=c1sol,c[0]=c0sol,eqinv)); |
> | op(4,%); |
> | indets(%); |
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