Solve[y'[x] == -(224.8 ((y[x]^2 - y[x]/10^11 - (0.000010385 x^3)/E^(2 x))/x^2)), y[x], x]

{y[x] -> 0.0022242 x^2 (2.248*10^-9/x^2 - (1. Sqrt[5.0535*10^-18 +   2.09923
E^(-2. x) x^3 - 899.2 x^2 Derivative[1][y][x]])/x^2)},
{y[x] -> 0.0022242 x^2 (2.248*10^-9/x^2 + Sqrt[5.0535*10^-18 + 2.09923 E^(-2. x) x^3 -
899.2 x^2 Derivative[1][y][x]]/x^2)}}[![Plot of y vs x by Wolfram Alpha][1]][1]