Question

(dy/dx) = (y-4)^2

Answer 1

\[(dy/dx) = (y - 4)^{2}\]

Answer 2

The problem can be written in the form x + f(y) = C

Answer 3

1/3 (y-4)^3 + C

Answer 4

you're solving for the integral right?

Answer 5

i have to find f(y)

Answer 6

like in the form x + f(y) = C

Answer 7

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.

Answer 8

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.

Answer 9

good zeh.........