verify tat y=x|x| is a solution to y'=2(|y|)^(1/2)
the absolute value is driving me nuts T.T

Question

verify tat y=x|x| is a solution to y'=2(|y|)^(1/2)
 >> the absolute value is driving me nuts T.T

anonymous · Answer

Split it up into piece-wise functions using the definition of absolute value.
Then see what happens to each piece.

anonymous · Answer

Case 1:  $x>0$:$$
|x|x = x^2
$$And then $y'=2x$, So show $$
2x=2(|x^2|)^{1/2}
$$

anonymous · Answer

sorry im late. i was forced to eat lunch just now.
i tried the first case, but how do i solve the |x| in 2x=2(|x^2|)^1/2
and for the 2nd case, is it -x^2?

hartnn · Answer

you need to show that 2x = 2 |x^2|^1/2 
so, x^2 is positive always, so |x^2| = x^2,
then just use $\Large (x^m)^n=x^{mn}$
to show that 
$(x^2)^{1/2}=x$

and yes, in 2nd case, it is -x^2.

anonymous · Answer

at last!! i got it :D
Thanks a LOT
i got for 0 for both. so tat means the function is a solution to the DE.
but is there a possibility in other question similar to this that i may get one of the cases does not equals to zero? then will the the function be a solution or not?

hartnn · Answer

yes, it may happen, and in that case the function will NOT be the solution.