Question

Show that....

Answer 1

Show that \[y=x ^{-1}\]
is a solution to the non linear equation \[\frac{ dy }{ dx }+y ^{2}=0\]

Answer 2

We haven't studied non linear diff eq's yet so I'm not sure how to proceed.

Answer 3

Your only goal here is to show that y = x^(-1) satisfies that equation. This means that, when we plug in y = x^(-1) and its derivatives into the equation, we get some undeniably true result such as 0 = 0. Does that sound good?

Answer 4

The fact that it is nonlinear really doesn't change this fact. It might change the way we find our solutions if we needed to ourselves, but we already have the solution provided (y = e^(-1)). We just need to verify that it works!

Answer 5

Ok so for this one we take \[\frac{ d }{ dx}x ^{-1}=-x ^{-2}\]
and plug it in so:
\[-x ^{-2}+\left( x ^{-1} \right)^{2}=0\]
Which is a true statement, therefore \[y=x ^{-1}\] is a solution to \[\frac{ dy }{ dx }+y ^{2}=0\]

Am I on the right track here?

Answer 6

Yep, that sounds good to me!

Answer 7

Thanks!!

Answer 8

Glad to help. :)