Question

How do I solve this IVP problem. http://i.imgur.com/MJ62T.jpg

Answer 1

Oh yeah \[\beta\] is postive constant

Answer 2

Just wondering do I divide by t^2

Answer 3

Yes, you should divide it by \(t^2\).

Answer 4

\[x'(t) = \frac{x(t)}{t} + \frac{\beta \left(x(t)\right)^2}{t^2}\] Substitution should work.

Answer 5

\[x(t) = vt \implies x'(t) = v't + v\]

Answer 6

I hope you can do it from here.

Answer 7

Would it not be x(t)/t^2

Answer 8

No, try to think about it. *See the ODE*

Answer 9

I dont really understand, Initially I thought that I divided both terms by \[t^{2}\]

Answer 10

\[t^2 x'(t) = x(t) ( t +\beta x(t))\]Now divide by \(t^2\).

Answer 11

\[x'(t)=x(t)/t*(\beta x(t))\]

Answer 12

No wait

Answer 13

\[t^2 = tx(t) + \beta (x(t))^2\]

Answer 14

Oh wait I get it now, thanks!