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# Easy differential equation

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1. The question asks to solve the ODE given that .
Is the solution which would be valid for OR
Is the solution just which is valid for |x|<1?
2. Anyone?
3. (Original post by Ano123)
The question asks to solve the ODE given that .
Is the solution which would be valid for OR
Is the solution just which is valid for |x|<1?

So the solution is negative of what you have and it is valid for
4. (Original post by NotNotBatman)

So the solution is negative of what you have and it is valid for
So in logarithmic form do we still need the absolute value in the log?
5. (Original post by Ano123)
So in logarithmic form do we still need the absolute value in the log?
No. Hopefully you can see that any of x substituted such that or will have a positive argument in the logs, so there is no need for the absolute value.
6. (Original post by NotNotBatman)
No. Hopefully you can see that any of x substituted such that or will have a positive argument in the logs, so there is no need for the absolute value.
x=1/2 gives a negative argument in the log.
7. (Original post by Ano123)
x=1/2 gives a negative argument in the log.
Typo, now corrected.
8. (Original post by NotNotBatman)
Typo, now corrected.
Does satisfy the ODE for |x|>1? Is this not a valid solution?

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