Question

Verify implicit solution
dX/dt=(x-1)(2x-1), ln(2x-1/x-1)=t

Answer 1

\[\ln(\frac{2x-1}{x-1})=\ln(2x-1)-\ln(x-1)\]

Answer 2

t=ln(2x-1)-ln(x-1)

Answer 3

\[\frac{d}{dt}[t]=\frac{d}{dt}[\ln(2x-1)-\ln(x-1)]\]

Answer 4

Yeah you're right:)

Answer 5

i'm getting a negative somewhere just writing it out

Answer 6

\[1=\frac{2}{2x-1}\frac{dX}{dt}-\frac{1}{x-1}\frac{dX}{dt}\]

Answer 7

\[1=(\frac{2}{2x-1}-\frac{1}{x-1})\frac{dX}{dt}\]

Answer 8

\[1=\frac{2(x-1)-1(2x-1)}{(2x-1)(x-1)}\]

Answer 9

\[1=\frac{2x-2-2x+1}{(2x-1)(x-1)}\]

Answer 10

\[1=\frac{-1}{(2x-1)(x-1)}\]

Answer 11

dX/dt of course

Answer 12

\[1=\frac{-1}{(2x-1)(x-1)}\frac{dX}{dt}\]

Answer 13

\[-(2x-1)(x-1)=\frac{dX}{dt}\] ? was everything done right? is this an error in the book?

Answer 14

Yeah you have done everything correctly

Answer 15

so it's an error in the book? as -(2x-1)(x-1) does not equal (2x-1)(x-1)

Answer 16

Yeah

Answer 17

i'll have my teacher know lol