- #1
roymkim
- 4
- 0
I have a Wronskian Question?
If the Wronskian W of f and g is t^2*e^t and if f(t)=t, find g(t).
I have tried setting up this problem:
tg'-t'g = t^2*e^t
tg'-g = t^2*e^t
Setting up the integrating factor, µ= e^∫-1 --> µ= e^-t
(e^-t)t*g' - (e^-t)*g = (e^-t)(t^2*e^t)
so preferably I would want to be able to set up the equation as (fg)' = (e^-t)(t^2*e^t)
but the derivative of (e^-t)t is not (e^-t).
The answer is supposed to be te^t+ct
If the Wronskian W of f and g is t^2*e^t and if f(t)=t, find g(t).
I have tried setting up this problem:
tg'-t'g = t^2*e^t
tg'-g = t^2*e^t
Setting up the integrating factor, µ= e^∫-1 --> µ= e^-t
(e^-t)t*g' - (e^-t)*g = (e^-t)(t^2*e^t)
so preferably I would want to be able to set up the equation as (fg)' = (e^-t)(t^2*e^t)
but the derivative of (e^-t)t is not (e^-t).
The answer is supposed to be te^t+ct