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Differential equation what going on? 
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#1
Mar1809, 12:11 PM

P: 64

Hi could someone explain why this result occurs when solving this differential equation.
dx/dt= xt 1/xdx/dt=t then intergrating both side we get with respect to dt we get, Inx=t^2/2 + c now this is the bit i don't understand why does the answer then become, x=Ce^2/t^2 I get really confused how the equation gets rearranged into the above form after the intergration has occured. Any help please? Thanks James 


#2
Mar1809, 02:24 PM

P: 1,635




#3
Mar1809, 02:28 PM

P: 64

Thanks but how come it is c*the e and then raised to the power of 2/t^2. Is that just a rule of exponentials?
Please help doing my head in!! Thanks James 


#4
Mar1809, 02:56 PM

Sci Advisor
HW Helper
Thanks
P: 26,157

Differential equation what going on?
No, x = Ce^{t2/2} … C is e^{c}. 


#5
Mar1809, 04:22 PM

P: 18

Hey James
dx/dt= xt dx/x = t·dt Ln(x) = (t^2)/2 + K x=e ^{ t2 /2 +K} = e ^{ K } · e ^{ t2 /2 } If we say that e^K = C then; x= C·e ^{ t2 /2 } I hope it helps 


#6
Mar1809, 08:39 PM

P: 64

Thanks all for your help got it now!! thanks again james : )



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