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anonymous
 one year ago
Write a DE in the form dy/dt=ay+b ;y=2/3 t>0
1) dy/dt=a(y+b/a)
2)dy/(y+b/a)=a dt
I understand why it integrates as but do not understand why the there is a ln(c) and not +c on both sids.
3)ln(y+b/a)ln(c)=a*t
anonymous
 one year ago
Write a DE in the form dy/dt=ay+b ;y=2/3 t>0 1) dy/dt=a(y+b/a) 2)dy/(y+b/a)=a dt I understand why it integrates as but do not understand why the there is a ln(c) and not +c on both sids. 3)ln(y+b/a)ln(c)=a*t

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Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Can you take a snapshot of the original problem?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0minus ln(c) is still subtract a constant why can't it take this form?

phi
 one year ago
Best ResponseYou've already chosen the best response.1first , if you have +c1 and +c2 on both sides, you can combine them into , for example, +c2c1 and rename that as C (an arbitrary constant) so people usually put the +C on only one side

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Why is it ln(c). It does not seem very intuitive.

freckles
 one year ago
Best ResponseYou've already chosen the best response.0I think they wrote the constant as ln(c) so they can write the left hand side as one term

freckles
 one year ago
Best ResponseYou've already chosen the best response.0\[\ln(y+\frac{b}{a})\ln(c) = \ln(\frac{y+\frac{b}{a}}{c})\]

phi
 one year ago
Best ResponseYou've already chosen the best response.1second, ln(C) is also arbitrary. they are doing that because usually what we do is ln y = x + C make each side the exponent of e y = e^(x+C) y= e^C * e^x and e^C is renamed an arbitrary constant , A (for example) y = A e^x

phi
 one year ago
Best ResponseYou've already chosen the best response.1the idea is if you use ln(C) rather than c you can do some algebra, and simplify the answer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I thought there was some hidden rule

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That is just something that you have to train yourself to see?!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is ln(c) more of a substitute for C so that you can simplify easier?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0yes the C took on the form ln(c) just to write things prettier like

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0THANK YOU EVERYONE!!!
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