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Input:

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

Output:

{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

Using Wolfram Alpha I got nearly a correct plot but the raw wolfram alpha code also seems problematic can any one see this wolfram alpha issue also(Since it is very helpful if i can do some solutions by wolfram alpha also)

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  • 1
    $\begingroup$ Do you mean DSolve? $\endgroup$ – Chip Hurst Apr 22 '19 at 22:33
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As Chip suggested, you need DSolve. But if you want to plot it, you also need an initial condition. This is why the Wolfram Alpha plot shows multiple curves... they correspond to different initial conditions. Here's what I got to work:

result[x_] = 
  y[x]/.NDSolve[{y'[x]==-(224.8 ((y[x]^2-y[x]/10^11 
    - (0.000010385 x^3)/E^(2 x))/x^2)), y[1] == 1}, y[x], {x, 0, 8}][[1]]
Plot[result[x],{x,1,8}];

enter image description here

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