anonymous
  • anonymous
(dy/dx) = (y-4)^2
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[(dy/dx) = (y - 4)^{2}\]
anonymous
  • anonymous
The problem can be written in the form x + f(y) = C
anonymous
  • anonymous
1/3 (y-4)^3 + C

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anonymous
  • anonymous
you're solving for the integral right?
anonymous
  • anonymous
i have to find f(y)
anonymous
  • anonymous
like in the form x + f(y) = C
ZeHanz
  • ZeHanz
Try separating variables:\[\frac{ dy }{ dx }=(y-4)^2 \rightarrow \frac{ dy }{ (y-4)^2 }=dx \]\[\int\limits_{}^{}\frac{ dy }{ (y-4)^2 }=\int\limits_{}^{}dx +C\]\[-\frac{ 1}{ y-4 }=x+C\]Solve for y:\[\frac{ 1 }{ y-4 }=C-x\]\[y-4=\frac{ 1 }{ C-x }\]\[y=\frac{ 1 }{ C-x }+4\]Where C is a real constant.
ZeHanz
  • ZeHanz
If 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:\[x+-\frac{ 1 }{ y-4 }=C\]This means:\[f(y)=-\frac{ 1 }{ y-4 }\] 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.
anonymous
  • anonymous
good zeh.........

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