For the equation:

$\displaystyle dv/dt=-kx^{1/2}$

I do not seem to be able to solve this one to find the general solution! :S

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- Feb 17th 2010, 10:57 AMYehiaTo find a solution to this Differential Equation?
For the equation:

$\displaystyle dv/dt=-kx^{1/2}$

I do not seem to be able to solve this one to find the general solution! :S - Feb 17th 2010, 11:43 AMpickslides
Are you sure that is the equation?

could it be $\displaystyle \frac{dv}{dt}=-kt^{1/2}$

or

$\displaystyle \frac{dv}{dt}=-kv^{1/2}$ ? - Feb 17th 2010, 12:42 PMYehia
- Feb 17th 2010, 12:46 PMpickslides
Happy to kick it off for you

$\displaystyle \frac{dv}{dt}=-kv^{1/2}$

separating the variables you get

$\displaystyle \frac{dv}{v^{1/2}}=-k~dt$

Now integrate both sides

Hint: $\displaystyle \int \frac{dv}{v^{1/2}} = 2v^{1/2}$ - Feb 17th 2010, 12:54 PMYehia
- Feb 17th 2010, 01:43 PMpickslides
How did you get that?

I get $\displaystyle v = \left( \frac{-kt+C}{2}\right)^2$