- #1
Joseph1739
- 33
- 0
Suppose I'm at this point in solving a differential equation and the initial condition is Q(0) = Q0
-ln|25-Q| + c1 = rt/100 + c2
Then if I combine c2-c1, I can rename it to c, we have:
-ln|25-Q| = rt/100 + c
Now if I multiply the equation by (-1), I get:
ln|25-Q| = -rt/100 - c
If I let -c = C:
ln|25-Q| -rt/100 +C
But if I rewrite -c = C, all the signs are reversed when I solve for Q. Also solving for the constant, my book kept the -c, and got c = Q0-25, but when I rewrite -c to C, I get C = 25-Q0.
So my question is, when can I rename constants? When I combined two constants it is okay to to rename the constant, but why is it incorrect when I negate a constant and rename it?
-ln|25-Q| + c1 = rt/100 + c2
Then if I combine c2-c1, I can rename it to c, we have:
-ln|25-Q| = rt/100 + c
Now if I multiply the equation by (-1), I get:
ln|25-Q| = -rt/100 - c
If I let -c = C:
ln|25-Q| -rt/100 +C
But if I rewrite -c = C, all the signs are reversed when I solve for Q. Also solving for the constant, my book kept the -c, and got c = Q0-25, but when I rewrite -c to C, I get C = 25-Q0.
So my question is, when can I rename constants? When I combined two constants it is okay to to rename the constant, but why is it incorrect when I negate a constant and rename it?