Albert Einstein is the greatest scientist in this century. Because of the greatness, he lifted by his follower as prophet of siences. So didn’t suprise if action of other scientist looked into justify his theory. Masya Allah, this is really abundant. Why? Ya, because in towards the prestisius throne of real sicence, Einstein is not only walks besides do small running („sai“ in term arabic), but he beforehand rides a delman Phytagoras and then takes a rides binomial bus. This statement not without a reason, because in mathematics context, the problem of special relativity only to be form of exploitation from Phytagoras theorem. Greatness of Einstein which is praiseworthy is his excess in exploiting the binomial approach of which is not thinking of other scientist. The fact, his special relativity only applied to movement of object which its speed (v) closing the velocity of light ().
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Einstein geverns his theory using simple mathematics not in differential equation. But why do you attempt to compare Einstein’s mathematics with yours?
Okey Mr.Antoni, we are waiting another comments. Thank’s.
Dear, All
I read on the internet how to solve the following Bernoulli DE (differential equation) :
y’ + y = xy3
which it solution is as follow :
let w = y(1-n) = y1-3 = y-2
dw/dy = -2y-3
(y’ + y = xy3 ) * dw/dy
w ‘ + yw’ = -2x
w’ + (y*-2y-3 ) = -2x
w’ + ( -2y-2 ) = -2x
Remeber that y-2 = w
w’ – 2w = -2x
solve using integrating factor: – h(x) = e∫ -2 dx = e-2x
-h(x) = e2x
w(x) = -h(x) * ∫ h(x) * -2x dx
w(x) = e-2x * -2∫ e-2x *x dx
w(x) = e-2x * -2(x*e-2x / 2 – e-2x / 4 + C )
w(x) = e-2x * (- x*e-2x + e-2x / 2 + C )
w(x) = [e-4x((1/2) – x] + Ce-2x )
given that
w(x) = y-2
1/y2 = [e-4x((1/2) – x] + Ce-2x )
Hence, the final solution is in the form :
y = 1/√ ( [e-4x((1/2) – x] + Ce-2x )
I think the alternative way for solving of the above Bernoulli differential equation can be performed using a smart method (http://www.rohedi.com) a so-called SMT (Stable Modulation Technique). Can anyone use the SMT to simplify the above problem?
Goodluck Mr.AF(A)
Wow keren…..
In your statement at a moment, mr.Rohedi capable to give alternative solution form of differential equation. How about with the following form mr?
dy/dx + 4*y*x^3 = -2*(x*y)^3,
for the every initial values x0 and y0.
Thanks mr.