anonymous
  • anonymous
dy/dx=y-2y^2
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
and what do you want?
amistre64
  • amistre64
ode :)
anonymous
  • anonymous
solution equation, initial condition is (0,100) i only need a hint on finding:\[\int\limits_{}^{}1\div(y-2y ^{2})\] i dont want much more help beyond that

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anonymous
  • anonymous
I'm not so into the integrals, sorry.
amistre64
  • amistre64
y' = y -2y^2 it looks like youd just reintegrate each term seperately
anonymous
  • anonymous
that was the starting equation, i then wrote it as dy/dx and then dy/y-2y^2=dx
anonymous
  • anonymous
i cant figure out how to take the integral of 1/(y-2yy)
amistre64
  • amistre64
helps if I keep track of the problem I spose :)
amistre64
  • amistre64
wiat, which equation you wanting to suit up?
anonymous
  • anonymous
I think you should use partial fractions
anonymous
  • anonymous
oh, ok y'=y-2y^2 dy/dx=y-2y^2 dy=(y-2y^2)dx dy/(y-2y^2)=dx integrate both
anonymous
  • anonymous
ahhh partial fractions!!! that should do it! thanks!!
anonymous
  • anonymous
aww yeah
anonymous
  • anonymous
that gives me an imaginary constant of integration -.-
anonymous
  • anonymous
lol, did the integral work out though? I didn't really read the problem
amistre64
  • amistre64
would y=e^x ??
amistre64
  • amistre64
and by that I mean: y = e^x + e^2x +C ?? just wondering
amistre64
  • amistre64
e^x - e^x^2....
anonymous
  • anonymous
hold on, ill upload a picture in a sec
anonymous
  • anonymous
can you just injtegrate the original equation (y'=y-2y^2) to (f(y)+c=1/2 y^2 - 2/3 y^3)
anonymous
  • anonymous
?
anonymous
  • anonymous
I don't see why not, and then use you initial condition for c.
anonymous
  • anonymous
uilfha thats pathetic, why bother doing the whole dy/dx sub when i could do that ><
anonymous
  • anonymous
And then I guess solve 0=1/2(100)^2-2/3(100)^3+c for c?
anonymous
  • anonymous
thats like -661,666.66...
anonymous
  • anonymous
lol, that whats confusing me. But that seems to be what they mean by the initial condition (0,100) , and thats how you would do it if you wanted the equation for x(y)

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