Question: How to solve auxiliary equation to find the families

Hi, I'm trying to solve auxilary equation to find its familes but I don't know what I'm doing wrong as I'm using following code:

famtemp := (diff(z(xi), xi))^2-a*z(xi)^2-b*z(xi)^3-c*z(xi)^4;

fam1 := simplify(`assuming`([dsolve(famtemp)], [b::real, a::real, c::real, -4*a*c+b^2 > 0, a > 0]))

I want to get the following family:

fam1 := 2*a*sech(sqrt(a)*xi)/(sqrt(-4*a*c+b^2)-b*sech(sqrt(a)*xi));

I hope someone will help me to solve it.


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