Plot global maximum point and differential equation

I have two questions:

(1) I found the global maximum point of the following function

FindMaximum[(Exp[-x^2/18]/3 + Exp[-(x - 5)^2/2] +
Exp[-(x - 15)^2/8]/2)*(1 + x^2)*Pi/(3 Sqrt[2 Pi]), {x, 15}]

but I can't plot the maximum point.

(2) I tried to solve the first-order nonlinear differential equation:

DSolve[{x^2 y'[x]+x y[x]==Exp[-x y[x]],y==0},y[x],x]

but I can't get the solution. Then, I have to plot the solution.

f[x_] := (Exp[-x^2/18]/3 + Exp[-(x - 5)^2/2] + Exp[-(x - 15)^2/8]/2)*(1 +
x^2)*Pi/(3 Sqrt[2 Pi])

max = FindMaximum[f[x], {x, 15}]

(* {48.8444, {x -> 15.5135}} *)

Plot[f[x], {x, 0, 20},
Epilog -> {Red, AbsolutePointSize,
Tooltip[Point[{x, f[x]}], {x, f[x]}] /. max[]}] eqn = {x^2 y'[x] + x y[x] == Exp[-x y[x]], y == 0};

sol = DSolve[eqn, y, x][] // Quiet

(* {y -> Function[{x}, Log[1 + Log[x]]/x]} *)

Verifying,

eqn /. sol // Simplify

{* {True, True} *)

FunctionDomain[y[x] /. sol, x]

(* x > 1/E *)

max2 = NMaximize[{y[x] /. sol, x > 1/E}, x]

(* {0.26438, {x -> 2.14518}} *)

Limit[y[x] /. sol, x -> Infinity]

(* 0 *)

Plot[y[x] /. sol, {x, 0.5, 10},
PlotRange -> {-0.5, 0.3},
Epilog -> {Red, AbsolutePointSize,
Tooltip[Point[{x, y[x]}], {x, y[x]}] /. sol /. max2[]}] 