Question

Differential Equation.

Answer 1

\[(x-2)\frac{ dy }{ dx }-y=(x-2)^3\]

Answer 2

Seems like it might be an integrating factor question.

Answer 3

p(x) = 1/x-2)?

Answer 4

put it in standard form

Answer 5

and be careful with the signs..

Answer 6

mu(x)=1/x-2

Answer 7

\[\frac{ dy }{ dx } +\left( \dfrac{-1}{x-2}\right)y=(x-2)^2\]

Answer 8

\[\frac{ dy }{ dx } - \frac{ y }{ (x-2) } = (x-2)^2\]
\[e^{\int\limits_{}^{}-\frac{ 1 }{ x-2 }=-\ln(x-2)=} (x-2)^{-1}\]

Answer 9

looks good ^

Answer 10

\[\frac{ d }{ dx }(y(x-2)^{-1}) \]?

Answer 11

=
\[\int\limits_{}^{}(x-2 )dx = \frac{ x^2 }{ 2 }-2x\]

Answer 12

All together.
\[y(x-2)^{-1} = \frac{ x^2 }{ 2 }-2x+c\]

Answer 13

Not sure about all that.

Answer 14

Explicitly for y?\[y = \frac{ x^2(x-2) }{ 2 }-2x(x-2)+c(x-2)\]

Answer 15

Perfect !

Answer 16

Seriously?

Answer 17

kindof.. :)

Answer 18

Lol thank you I think

Answer 19

you may want to verify it with wolfram to double(triple ?) check

http://www.wolframalpha.com/input/?i=%28x-2%29y%27-y%3D%28x-2%29%5E3

Answer 20

looks wolfram simplified the final answer a bit ^