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I entered the following into Mathematica:

p[x_] := 4 x
q[x_] := 4 Sqrt[x] - 3
f[x_] := E^-Sqrt[x]
DSolve[y''[x] + p[x] y'[x] + q[x] y[x] == f[x], y[x], x]
 DSolve[
    (-3 + 4 Sqrt[x]) y[x] + 4 x Derivative[1][y][x] + 
      (y^\[Prime]\[Prime])[x] == E^-Sqrt[x],
    y[x], x]

Why is Mathematica refusing to evaluate my DSolve expression?

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If DSolve doesn't evaluate and you have used correct syntax, that means DSolve is not aware of a symbolic solution to your differential equation.

You may want to find a numeric solution using NDSolve or using some kind of approximation to simplify the problem down.

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