- #1
Irid
- 207
- 1
Hi,
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?
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?