# Differential equation

1. Apr 18, 2014

### kyu

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

i got k = ln |9/64|

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

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2. Apr 18, 2014

### Staff: Mentor

3. Apr 18, 2014

### kyu

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)

4. Apr 18, 2014

### Staff: Mentor

Where did the dh go?
How did you get this (above)?

5. Apr 18, 2014

### pasmith

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 $\int x^{-1}\,dx = \ln |x| + C$.