Solve this differential equation and plot the solution?

Questions
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1

Hi
Could any one help me please to find the solution of this differential equation.

de.png
de.png404×157 2.23 KB

Its included in the Mathematica notebook

de.nb (34.7 KB)

2

Mathematica gives a correct, if complicated, symbolic answer in terms of an implicit function. You can extract the information and plot the solution this way:

sol = DSolve[y'[x] - Sqrt[20]/Sqrt[4 y[x]^(5/2) - 5 y[x]^2 + 1] == 0, 
   y[x], x];
f[y_, c_] = x /. First@Solve[sol[[1]] /. {y[x] -> y, C[1] -> c}, x];
xAsFunctionOfy[y_, c_] = f[y, c] - f[0, c];
ParametricPlot[{xAsFunctionOfy[y, 1], y}, {y, 0, 1}]
3

Thank you
I have learnt a lot from your advice, I really appreciate it. Regards