I bet this has asked before, but I can't seem to find an answer anywhere.

I have x and y functions which, individually plotted, are showing up fine, but when I try to plot the parametrically, the graph does not show up. I absolutely cannot figure out why this is occurring, and I've tried simpler functions (such as x=sin[t]), which work, leading me to believe it has something to do with the way I solved the differential equation.

    k1 = 9*^9*(1.6*^-19)^2;
    me = 511*^3;
    mp = 938*^6;
    ℏ = 6.59*^-1;
    U[r_] := -k1/r;
    V[r_] := U[r] + l[r]^2/2/μ/r^2;
    L := n*ℏ;
    ϕ'[r_] := L/me/r^2;
    F[r_] := -k1/r^2;
    μ = (me + mp)/(me*mp);
    u[ϕ_] := 1/r[ϕ];
    l[r_] := μ r^2 ϕ'[r];
    n = .1;

    sol = NDSolve[{D[D[u[ϕ], ϕ], ϕ] == 
         u[ϕ] - μ/l[r[ϕ]]^2/u[ϕ]^2*F[r[ϕ]], 
        r[1] == 30, r'[1] == 5}, r[ϕ], {ϕ, 0, 4 Pi}];

    X[ϕ1_] := r[ϕ]*Cos[ϕ] /. sol /. ϕ -> ϕ1;
    Y[ϕ1_] := r[ϕ]*Sin[ϕ] /. sol /. ϕ -> ϕ1;

    Plot[X[th], {th, 0, 2 Pi}]
    Plot[Y[th], {th, 0, 2 Pi}]
    ParametricPlot[{X[t], Y[t]}, {t, 0, 2 Pi}]
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Note the First@sol part:

X[ϕ1_] := r[ϕ]*Cos[ϕ] /. First@sol /. ϕ -> ϕ1;
Y[ϕ1_] := r[ϕ]*Sin[ϕ] /. First@sol /. ϕ -> ϕ1;

ParametricPlot[{X[t], Y[t]}, {t, 0, 2 Pi}, AspectRatio -> 1]

Mathematica graphics


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