# Thread: hlep with this diff. eq. pls

1. ## hlep with this diff. eq. pls

hello,

i have (dx/dt)^2 = (1/x^4) -1 and want to write an integral for t(x)...

(dx/dt) = +/- {x^2/[(1-x^4)^(1/2)]}

so t(x) = +/- integr of {x^2/[(1-x^4)^(1/2)]}

but the book says t = integr (from u=1 to =x) of {u^2/[(1-u^4)^(1/2)]}

can someone please help me see that the book has done here? thanks a lot!

2. Originally Posted by pepsi
hello,

i have (dx/dt)^2 = (1/x^4) -1 and want to write an integral for t(x)...

(dx/dt) = +/- {x^2/[(1-x^4)^(1/2)]}

so t(x) = +/- integr of {x^2/[(1-x^4)^(1/2)]}

but the book says t = integr (from u=1 to =x) of {u^2/[(1-u^4)^(1/2)]}

can someone please help me see that the book has done here? thanks a lot!
Please post the entire question, including the intial condition that came with the DE (I assume it was x = 1 when t = 0. But we shouldn't have to assume.)

Also, note that if $\frac{dt}{dx} = f(x)$ subject to the boundary condition $x = x_0$ when $t = t_0$ then $t(x) = \int_{x_0}^{x} f(u) \, du$.