Solving x"+(1/x^2)=0: Finding k,a,B

[fredrick08]

Homework Statement

x"=(-1/x^2) when x=c1>0 and x'=c2 at t=0 what relationship has to exist between c1 and c2 to give the problem a solution of k(t+B)^a... then solve for k,a,B...

The Attempt at a Solution

x"+(1/x^2)=0, I am sorry I am just stuck, i think it goin to look somthin like (x+2)^2... but this inverse square is confusing me... we normally do it like,

\lambda"+a\lambda=0, but I am not sure, can anyone please point me in the right direction... but then wat does it mean by what relationship between c1and c2?

 

[HallsofIvy]

The first thing you need to do is state the problem clearly. " x"= -1/x² when x= c1> 0" only gives x" at a single value of x. Did you mean "for x> c1"?

Rewrite the equation as x²x"= -x and see what happens when you replace x with k(t+B)^a.

 

[fredrick08]

na that's wat the question says... its definitely x=c1>0... huh i can't write it like that coz then it would be (x^2)x"=-1 not -x... wel doesn't that mean that c1=c2?