So I'm supposed to prove that(adsbygoogle = window.adsbygoogle || []).push({});

[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.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Help with nonlinear 1st order ODE

Loading...

Similar Threads - Help nonlinear order | Date |
---|---|

Need help solving second-order nonlinear differential eq | Feb 3, 2015 |

Need help for solving a 2nd order nonlinear differential equation | Feb 1, 2012 |

2nd order nonlinear ODE help needed | Dec 13, 2011 |

First order nonlinear differential equation Help needed. | Sep 7, 2011 |

Second order, nonlinear differential equation help | Sep 6, 2011 |

**Physics Forums - The Fusion of Science and Community**