Hello JacquesC, actually the problem doesn't occur in direct response to PDEtools[dchange], but when trying to impose a boundary condition for the point of the singularity. What I tried was the following: ctkd1 := diff(c(t),t) = 2*(c(t))^2 + 21/50*c(t) - 1/100*(h(t))^2 - 1/5*c(t)*h(t) - (9/2000)*h(t) + 49/4000: htkd := diff(h(t),t) = h(t)*(c(t) - 1/5*(h(t)-1)): ktkd := diff(k(t),t) = 28/100*k(t) - h(t) - 1/5*k(t)*h(t): rescale := [op(dchange(t=r/(1-r^2), [ctkd1, htkd, ktkd])), k(0)=55/6, k(1)=55/3, h(1)=11/10]; sol := dsolve(rescale,[c(r),h(r),k(r)], numeric); In response to the last command, Maple gives the error message Error, (in dsolve/numeric/bvp) system is singular at right endpoint, use midpoint method instead

Hello JacquesC, actually the problem doesn't occur in direct response to PDEtools[dchange], but when trying to impose a boundary condition for the point of the singularity. What I tried was the following: ctkd1 := diff(c(t),t) = 2*(c(t))^2 + 21/50*c(t) - 1/100*(h(t))^2 - 1/5*c(t)*h(t) - (9/2000)*h(t) + 49/4000: htkd := diff(h(t),t) = h(t)*(c(t) - 1/5*(h(t)-1)): ktkd := diff(k(t),t) = 28/100*k(t) - h(t) - 1/5*k(t)*h(t): rescale := [op(dchange(t=r/(1-r^2), [ctkd1, htkd, ktkd])), k(0)=55/6, k(1)=55/3, h(1)=11/10]; sol := dsolve(rescale,[c(r),h(r),k(r)], numeric); In response to the last command, Maple gives the error message Error, (in dsolve/numeric/bvp) system is singular at right endpoint, use midpoint method instead