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So I'm supposed to prove that

[itex]{x}^{.}(t) = x^{2}+ t^{2}[/itex] with [itex] x(0) = 0 [/itex] blows up before [itex] t = 1 [/itex].

I'm not sure what method to use to solve I've tried setting up an integral such as [itex]\int^{x(t)}_{x(0)} \frac{dx}{x^{2}+t^{2}} = \int^{t}_{0} dt[/itex] but I didn't think I could do this since 't' is varying over time on the Left Hand side and I'm integrating with respect to x.

The only other clue I have is to use a comparison ODE, which was mentioned in class, in which would use a function, say... [itex] g^{.}(t) =< x^{.}(t) [/itex] which was easier to work with. If I were able to prove that the lesser function exploded before [itex] t= 1 [/itex], then logically the greater one explodes. The thing is I don't know what function I would even chose to set this up. Any ideas?

..and Thank youuuuu.

[itex]{x}^{.}(t) = x^{2}+ t^{2}[/itex] with [itex] x(0) = 0 [/itex] blows up before [itex] t = 1 [/itex].

I'm not sure what method to use to solve I've tried setting up an integral such as [itex]\int^{x(t)}_{x(0)} \frac{dx}{x^{2}+t^{2}} = \int^{t}_{0} dt[/itex] but I didn't think I could do this since 't' is varying over time on the Left Hand side and I'm integrating with respect to x.

The only other clue I have is to use a comparison ODE, which was mentioned in class, in which would use a function, say... [itex] g^{.}(t) =< x^{.}(t) [/itex] which was easier to work with. If I were able to prove that the lesser function exploded before [itex] t= 1 [/itex], then logically the greater one explodes. The thing is I don't know what function I would even chose to set this up. Any ideas?

..and Thank youuuuu.

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