# Revision history [back]

### Logarithms and desolve

More questions about desolve results: Using

 y = function('y', x)
desolve(diff(y,x) == y*(100-y), y)


results in the solution:

-1/100*log(y(x) - 100) + 1/100*log(y(x)) == _C + x


But that solution does not work for y<100. But it is correct if you assume that it should be log(abs(y(x)-100)) in the first term. Is the abs() implicit?

### Logarithms and desolve

More questions about desolve results: Using

 y = function('y', x)
desolve(diff(y,x) == y*(100-y), y)


results in the solution:

-1/100*log(y(x) - 100) + 1/100*log(y(x)) == _C + x


But that solution does not work for y<100. But it is correct if you assume that it should be log(abs(y(x)-100)) in the first term. Is the abs() implicit?

(The log terms actually comes from the integral of 1/y and 1/(100-y) so it should be absolute values.)