losing solution while solving differential equation etc.

Hi

Please have a look on the following linked pages. You can find my queries there. Please help me with them. Thanks a lot.

Page #1: https://img839.imageshack.us/img839/5540/ppage1.jpg
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Regards
PG

Hi,

If i understand this question this might help...

Given an equation like this:
x^3+2*x^2+3*x=0

The first impulse is to divide both sides by x and get:
x^2+2*x+3=0

and then use the quadratic formula to solve for the *two* values of x. This gives us x1 and x2.

But we started with a third degree equation, so what happened to the third solution?
We seem to have lost it, and that happened because we divided both sides by the variable, x.
The 'lost' solution is zero, and is better found by first factoring:
x*(x^2+2*x+3)=0

and now it is plain to see that if x is zero, we certainly satisfy this equation, so zero is also a valid solution.

This thing happens a lot when we divide by the variable or one of its powers in order to obtain a solution.