Solving Differential Equation: ln |9/64| = k

[kyu]

i got k = ln |9/64|

then how can the next step using ln 0 doesn't make sense. what should i do?

 

[Mark44]

i got k = ln |9/64|

then how can the next step using ln 0 doesn't make sense. what should i do?

Please show us your work.

 

[kyu]

Please show us your work.

should be wrong but here goes

dh/dt = -k h^(1/2)
1/h^(1/2) = -k dt
ln 9 - ln 64 = k
ln |9/64| = k

ln 0 - ln 64 = ln |9/64| (t-0)

 

[Mark44]

should be wrong but here goes

dh/dt = -k h^(1/2)
1/h^(1/2) = -k dt

Where did the dh go?

ln 9 - ln 64 = k

How did you get this (above)?

ln |9/64| = k

ln 0 - ln 64 = ln |9/64| (t-0)

 

[pasmith]

should be wrong but here goes

dh/dt = -k h^(1/2)
1/h^(1/2) = -k dt
ln 9 - ln 64 = k
ln |9/64| = k

ln 0 - ln 64 = ln |9/64| (t-0)

The integral of $h^{-1/2}$ is given by the usual rule for powers, $\int x^\alpha\,dx = \frac{x^{\alpha + 1}}{\alpha + 1} + C$, not the exception $\int x^{-1}\,dx = \ln |x| + C$.