Find g(t) Given Wronskian and f(t)=e2t

[Success]

If the Wronskian W of f and g is 3e^4t, and if f(t)=e^2t, find g(t).

Here's the work:
e^2tg'(t)-(e^2t)'g(t)=3e^4t
e^2tg'(t)-2e^2tg(t)=3e^4t
g'(t)-2g(t)=3e^2t
p=-2
e^integral of p=e^-2t
g(t)=?

 

[1MileCrash]

I think you should leave the posting template, it's listed in the rules of the forum.

But anyways, it looks like you've shown that g(t) satisfies a linear differential equation. It also looks like you've listed an integrating factor of e^(∫-2 dt).

So, you're pretty much done. Do you know how to apply an integrating factor to solve a linear differential equation?

 

[Success]

Thanks, I've already solved it.