# Thread: Absolute values in differential equations.

1. ## Absolute values in differential equations.

Hi,

I've been taught that when integration involves logs like $\displaystyle y=\int\frac{1}{x}\ dx$, you must express your answer as the log of an absolute value unless that value is known to be positive. e.g. in this case $\displaystyle y=log_e\left | x \right |+c$.
But in my textbook, it rarely uses absolute values, and just states the answers in the form $\displaystyle y=log_e(x)+c$, which then obviously changes the solutions to many differential equations.

Am I right to use the absolute value, or am I missing something?

I've been taught that when integration involves logs like $\displaystyle y=\int\frac{1}{x}\ dx$, you must express your answer as the log of an absolute value unless that value is known to be positive. e.g. in this case $\displaystyle y=log_e\left | x \right |+c$.
But in my textbook, it rarely uses absolute values, and just states the answers in the form $\displaystyle y=log_e(x)+c$, which then obviously changes the solutions to many differential equations.