Manipulating a Differential equation

Question

I want to manipulate a differential equation, but I am not getting any graph for it. The following is the code that I have used.

P[t_, a_, b_, c_, d_] = p[t] /.First@NDSolve[{p'[t] - (a*p[t]^2) - b*p[t] + c*(p[t]^(1 - d)) == 0, 
p[0] == 1}, p, {t, 0, 0.335}]; Manipulate[Plot[P[t, a, b, c, d], {t, 0, 0.335}, 
PlotLabel -> P[x, a, b]], {{a, 1, "a"}, -10, 10, 
Appearance -> "Labeled"}, {{b, 1, "b"}, -5, 5, 
Appearance -> "Labeled"}, {{c, 1, "c"}, -5, 5, 
Appearance -> "Labeled"}, {{d, 1, "d"}, -5, 5, 
Appearance -> "Labeled"}]

Note, the differential equation reaches singularity quite quickly, one of the reason why I have used t=0.335 in the code.

Need Help, Thanks in advance

Answer 1

ParametricNDSolve can be helpful:

Manipulate[
 Plot[f[p1, p2, p3, p4][t], {t, 0, 0.3}, PlotRange -> {-1, 10}],
 {{p1, 1, "a"}, -10, 10, Appearance -> "Labeled"}, {{p2, 1, "b"}, -5, 
  5, Appearance -> "Labeled"}, {{p3, 1, "c"}, -5, 5, 
  Appearance -> "Labeled"}, {{p4, 1, "d"}, -5, 5, 
  Appearance -> "Labeled"},
 Initialization :> (
   f = p /. 
     ParametricNDSolve[{p'[t] - (a*p[t]^2) - b*p[t] + 
         c*(p[t]^(1 - d)) == 0, p[0] == 1}, 
      p, {t, 0, 0.335}, {a, b, c, d}])]