# Math Help - find x(t) : ( a - x(t) )^2 = c*x'(t)

1. ## find x(t) : ( a - x(t) )^2 = c*x'(t)

hello everyone, im trying to do a voltage analysis for some electric circuit in my homework assingment and deduced the following equation:

(a - v(t) )^2 = c*v'(t)

a,c - constants
now i dont remember much from the differential equations course i took in first year, but i dont think we learned how to solve a none linear equation

so can anyone explain to me how to solve such a thing ?

thanks

2. It's separable...

So $\displaystyle (a - v)^2 = c\,\frac{dv}{dt}$

$\displaystyle \frac{1}{c} = (a - v)^{-2}\,\frac{dv}{dt}$

$\displaystyle \int{\frac{1}{c}\,dt} = \int{(a - v)^{-2}\,\frac{dv}{dt}\,dt}$

$\displaystyle \int{\frac{1}{c}\,dt} = \int{(a - v)^{-2}\,dv}$.

You should be able to solve now.

3. oh right !!, thats how u do that

thanks man