Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I was solving my own-invented physical problem, and obtained a differential equation

[tex]\frac{dx}{dt} = k \sqrt{t-x^2}[/tex]

with k positive constant. I wish to solve it. I'm unable perform separation of variables here, and power-series method works poorly, too. I conclude that this equation does not have any closed-form or familiar series solution, so the best thing that I could do is use numerical methods [of an Excel type, but Gnumeric is my choice :)]. It turned out that with k=1, when t=1, x=0,6, exacty. This gives a clue that there might exist some sort of a solution (or it might not be any kind of a clue, I'm just being silly). How do I find it? How do I solve this equation?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

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

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

# Homework Help: Differential equation I can't solve

**Physics Forums | Science Articles, Homework Help, Discussion**