Calculus differential equations:
If dx/dt= (2t+1)/(2x) and x(1)=3 find x(0)
Please help!

Question

Calculus differential equations: 
If dx/dt= (2t+1)/(2x) and x(1)=3 find x(0)
Please help!

anonymous · Answer

I'm not sure how I should start, should I try to separate and integrate?

phi · Answer

rewrite it as
2x dx = (2t+1) dt

anonymous · Answer

ok and then integrate each side... let me do that
pretty basic so far, I'm just not sure what to do after that
ah, give me a few seconds to integrate

anonymous · Answer

x^2= t^2 +t +C ?

phi · Answer

yes.
now you need to find C
use  t=1  , x=3

mathmale · Answer

Looks good!  
Now use the initial condition, x(1)=3, to determine your constant of integration.  In other words, take your own equation (above), and let t=1 and x=3.  C will be the only variable left.  You can calculate C from this equation.

anonymous · Answer

ok so sub in and C= 7

phi · Answer

now solve for x when t=0

anonymous · Answer

with this equation?
x^2= t^2 +t +C
x^2 = 0 +0 +7
x= sqrt7?

phi · Answer

yes

anonymous · Answer

wow thank you, you made it so easy! Would you help me with one more of this type please?