Write a DE in the form dy/dt=ay+b ;y=2/3 t->0
I understand why it integrates as but do not understand why the there is a -ln(c) and not +c on both sids.
Stacey Warren - Expert brainly.com
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Can you take a snapshot of the original problem?
minus ln(c) is still subtract a constant
why can't it take this form?
first , if you have +c1 and +c2 on both sides, you can combine them into , for example, +c2-c1
and rename that as C (an arbitrary constant)
so people usually put the +C on only one side
second, 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
the idea is if you use ln(C) rather than c
you can do some algebra, and simplify the answer
I thought there was some hidden rule
That is just something that you have to train yourself to see?!
is ln(c) more of a substitute for C so that you can simplify easier?
yes the C took on the form ln(c) just to write things prettier like