I have the following question:
- The differential equation $\frac{dy}{dx} = \ln{y}-\ln{x}$ has a particular solution with $x=e, y=2e$. Show that $$\int_k^2 \frac{1}{\ln{v}-v} dv=1, $$ where $k$ is the value of $v$ when $x=1$.
That part is fine. However, I am then asked to find $k$ to three significant figures, and since I cannot evaluate the integral, I don't know how to do this...
Thank you for your help in advance,
C.G