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 re-arranged into the above form after the intergration has occured. Any help please? Thanks James
You are just exponentiating both sides of the equation. But remember that exponential functions and log's are inverse functions so e^lnx=x
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
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