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here the plot is b[a] vs. a.

w[a] is part of my differential equation and it depends upon a and c.

i have written the program the program for c=1 below. I want to plot for several other c values(like c=1/3,1/2 and 2/3) in the same plot. is it possible via mathematica?

c = 1;

w[a_] := 2*a^(3*(1 + c))/(1 + 2*a^(3*(1 + c)));

fun = 2/3 a^2 b''[a] + (1 - w[a]) a b'[

a] - (1 + w[a]) (1 - 3 c w[a]) b[a]

test = NDSolve[{fun == 0, b'[10^(-4)] == 0, b[10^(-4)] == 1},

b, {a, 10^-4, 10}]

LogLinearPlot[Evaluate[b[a] /. test], {a, 10^-4, 10},

PlotRange -> All]