Write and then solve for y = f(x) the differential equation for the statement: "The rate of change of y with respect to x is inversely proportional to y^4."

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Write and then solve for y = f(x) the differential equation for the statement: "The rate of change of y with respect to x is inversely proportional to y^4."

Mathematics
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hint: two quantities, say A and B are inversely proportional if the subsequent condition olds: A*B = k where k is a constant
holds*
dy/dx = ky^4 ?

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no, since that formula expresses the direct proportionality
hint: we can write this: A= dy/dx, and B=y^4
dy/dx = k/y^4
correct!
okay and now int(dy y^4) = int(dx k) (y^5)/5 = (x^2)/2 + C
\[y = \sqrt[5]{\frac{ 5x^2 }{ 2 } + C}\]
I got this: \[\Large \begin{gathered} \int {{y^4}dy} = \int {kdx} \hfill \\ \hfill \\ \frac{{{y^5}}}{5} = kx + C \hfill \\ \end{gathered} \]
doesn't the right side turn into \[\frac{ kx^2 }{ 2 } + C\]
no wait i see what i did wrong
okay so then \[y = \sqrt[5]{5kx + C}\]
correct!
sorry! I had to specify this: \[\Large C \in \mathbb{R}\] since you are searching for a real funtion
thank you so much :D
:)
quick question what does the \[\epsilon \] mean
in general, in mathematical analysis, the mathematicians use \epsilon in order to indicate a small and positive quantity, which, in some case goes to zero
okay , double thank you :D
:)

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