I have a Wronskian Question?If the Wronskian W of f and g is t^2*e^t

[roymkim]

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

 

[lurflurf]

The quotient rule is handy here
f g'-f' g=f²(g/f)'

f g'-f' g=t²(g/t)'=t²e^t

 

[roymkim]

I'm still not getting the right answer.

I get it down to (te^t)(t-1)+ct

 

[lurflurf]

Where are you getting that t-1? It clearly does not belong.