# Tagged Questions

94 views

### Unable to comprehend a connection between two equations

I was reading this paper and got stuck at the transition from Equation (13) to Equation (14) (p. 16/17). We got a function of the form: $y(t)=k(t)^{\alpha}h(t)^{\beta}$ We know it grows from zero ...
16 views

### Lipschitz continuity in two variables [duplicate]

Prove that $y \mapsto f(x,y)$ is Lipschitz continuous, where $$f(x,y) = \frac{y}{x} \ln{\frac{y}{x}}, \ \ \ |x-1| \leq \frac{1}{2}, |y-1| \leq \frac{1}{2}e$$ I tried to solve this, but I find it ...
42 views

### Absolute values in logarithms in a solution of differential equation

How have the moduli signs disappeared in the following step: $$\frac1{k}\left(\ln|g+kv| - \ln|g+ku|\right) = -t$$ Therefore $$\ln\left(\frac{g+kv}{g+ku}\right) = -kt$$ $g$, $k$ and $u$ are ...
45 views

### function symmetric around a point

I need some quick help solving this: What is y(ln(2))if the function y satisfies $$\frac{dy}{dx}=1-y^2$$ and is symmetric about the point (ln(4),0)? I know that a function is symmetric about the ...
52 views

### $100(1.2)^t=\alpha t$. How do I solve for t?

I'm playing with a population model, and I wondered how to find the $t$ when the population goes to zero, with regard to $\alpha$. I've ended up with this, and I don't know how to solve for t. Can ...