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 Aug2 comment hints on solving DE Yeah, can happen. ;-) Aug2 comment hints on solving DE Sorry for the $\frac{a}{2}$, it should be only a Aug2 answered hints on solving DE Aug2 comment hints on solving DE You must have made different substitutions. I am getting the following. $$\frac{dw}{dz} = \frac{w-\frac{a}{2}z}{z-aw}$$ I will write a partial answer for you. Aug2 comment hints on solving DE No, basically you then eliminate $x$ and $y$ and solve for $w$ in terms of $z$. If you want more hint, I can give you so. Aug2 comment hints on solving DE Try putting $w^{2} = x^{2} + y^{2} + z^{2}$ and then use the identity $$\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\frac{k_{1} a + k_{2} c + k_{3} e}{ k_{1} b+ k_{2} d+ k_{3} f}.$$ Aug1 awarded Yearling Jul31 comment Limit of binomial coefficient @J.M., Thanks for the info. Jul31 comment Limit of binomial coefficient @J.M. : He is using the notation for combination, so probably he means a non-negative integer? Jul30 comment Approximated Laplace transform of a non-linear system Jul30 comment Approximated Laplace transform of a non-linear system $\dot{\omega}(t) \approx \alpha_0 \omega(t) + \beta_0 i(t)$ is a valid assumption for only $t \approx 0$ since $\dot{\omega}(t)$ is largely negative and very large and stays like that until $\omega\left(t\right)$ is very small. So, that is one source of error. Jul30 comment Approximated Laplace transform of a non-linear system If you can give me approximate regions (in terms of actual values of $\omega$ and $i$ in which you want the solution, it might be better/easier to solve. I can solve it most probably even if you are able to provide the value of $\omega(t)$ as $t \rightarrow \infty$. Jul29 comment Open mapping of the unit ball into itself Ohh, right. Sorry. I missed the open part. So careless of me. Jul28 revised Methods to solve differential equations added 755 characters in body Jul28 revised Methods to solve differential equations added 755 characters in body Jul28 answered Methods to solve differential equations Jul28 comment Methods to solve differential equations I guess that we can do so, is guaranteed by the fundamental theorem of calculus involving Riemann Sums, showing that they are equivalent to the integral and that integration is inverse of differentiation. Jul27 comment How to make notes when learning a new topic I have tried taking notes in LaTeX and unless you are taking lecture notes, which is mostly text and formatting, it is not really worth it. I never have been able to take lecture notes myself however. Though, some people have been apparently very successful. I also have a very bad handwriting, so I get what you are saying, but it (Live-TeXing) has been a big failure for me. mathoverflow.net/questions/12638/… Jul27 comment Is there a bijection between mathematical structures and morphisms that preserve this structures forming a category? Just for clarification, since I am also new to the field. The OP is suggesting that we create a set $A$ of all the structures and set $B$ of all the morphisms and then show that there is a one-to-one correspondence between $A$ and $B$ right? Jul26 revised Approximate solution for the root of a non-linear function added 10 characters in body