Question

Find the error. Calculus II's most confusing group work. No one in class got it today.

Answer 1

http://uni.dougshaw.com/findtheerror/FTEgrowth.html

Answer 2

I think the error is somewhere near:
dy/dx = ky --> y = k(dx)

Answer 3

any ideas SithsAndGiggles?

Answer 4

\[\int\frac{dy}{y}=\ln|y|+C\not=\ln y+C\]

Answer 5

So it was just missing abs val bars

Answer 6

Essentially, yes.
\[\begin{align*}\ln|y|&=kx+C\\
e^{\ln|y|}&=e^{kx+C}\\
|y|&=Ae^{kx}
\end{align*}\]
You can't have \(y=0\) because \(\ln 0\) is undefined, which means \(A\not=0\).

Since \(|\text{anything}|\ge0\), then \(A>0\) exclusively.

Answer 7

Cool beans