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anonymous
 3 years ago
(dy/dx) = (y4)^2
anonymous
 3 years ago
(dy/dx) = (y4)^2

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[(dy/dx) = (y  4)^{2}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0The problem can be written in the form x + f(y) = C

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0you're solving for the integral right?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0like in the form x + f(y) = C

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Try separating variables:\[\frac{ dy }{ dx }=(y4)^2 \rightarrow \frac{ dy }{ (y4)^2 }=dx \]\[\int\limits_{}^{}\frac{ dy }{ (y4)^2 }=\int\limits_{}^{}dx +C\]\[\frac{ 1}{ y4 }=x+C\]Solve for y:\[\frac{ 1 }{ y4 }=Cx\]\[y4=\frac{ 1 }{ Cx }\]\[y=\frac{ 1 }{ Cx }+4\]Where C is a real constant.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0If you really want to rewrite it as \[x+f(y)=C\]in my calculation above, just before "solve for y" you could also write it as:\[x+\frac{ 1 }{ y4 }=C\]This means:\[f(y)=\frac{ 1 }{ y4 }\] In my view this is not an answer yet, because it is possible to get y as function of x, as you can see in the end of my calculation.
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