Gavran's latest activity

Clearly, the equation ## 4x^5u''+12x^2u'-4u=0 ## is not a Cauchy–Euler equation, and it cannot be solved by the standard method, which...

I would like to give a big thank you to @anuttarasammyak , @pasmith , @Gavran , and @DaveE for their inputs to this thread. I really...

Analytical solution by using Vieta's substitution: ## \begin{align} &a^3-9a^2+21a-3=0\nonumber\\...

@Gavran Very good=Excellent. :) You have an interesting approach where you translated the first curve by ## (a,b) ## until it made...

Let ## (x_1,y_1) ## be a point on the curve ## f(x)=4-x^2 ##, which is the closest point on the curve ## f(x) ## to the curve ##...

The other day a friend of mine gave me the above problem which I found rather interesting. I was able to get a numerical solution...

There are Figures 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, and 19 in the same text...

Ok, there must be some rule I’m missing, after which the penny will drop. Forgive my stupidity. How is the X1 (or U) junction defined...

It depends on how X1, X2, and X3 are interconnected with W4, W5, and W6. See again Figure 4-D7 (the third image on the right).

Yes, you are right. That means X1 lags H1 by 30° in group 1, and X1 lags H1 by 330° in group 11. Both examples are correct. See Figure...

Thanks, so by that definition the group 1 will be a 30°, and the group 11 a 330°? There were two other examples: I make these group 7...

This is group 1. If H1 points at 12 o'clock, X1 will point at 1 o'clock. This is group 11. If H1 points at 12 o'clock, X1 will point at...

The substitution ## y_1=10^y ## simplifies the equation $$ 10^ydy=\frac{dx}{x\ln10} $$ to the equation ## dy_1=dx/x ##. The general case...

In the general case, the time that the ant needs to reach the end of the rope is $$ T=\frac cv(e^\frac v\alpha-1) $$, where ## c ## is...