Find particular solution to differential equation. 5y'(t) + 10y(t) = 2e^-t

Question

anonymous · Answer

Are you familiar with method of integrating factor?

anonymous · Answer

I used to be (; I will look it up.

anonymous · Answer

I'll get you started!
$$p=10$$$$P= \int\limits 10~dt$$$$\mu = e^P$$

anonymous · Answer

Oops, I made a stupid mistake. Coefficient in front of the second order derivative must be 1!
$$\large p=5$$$$\large P=\int\limits 5~dt$$$$\large\mu=e^{5t}$$$$\large e^{5t}(y'+2y)=\frac{ 2 }{ 5 }e^{-t}e^{5t}$$$$\large (e^{5t}y)'=\frac{ 2 }{ 5 }e^{4t}$$

anonymous · Answer

Continue to solve for y!

anonymous · Answer

Shouldn't it be e^2t * y = Integral (e^2t)(2/5)(e^-t)
so y = (2/5)e^-t

anonymous · Answer

Yes, I'm sorry again, I can't even simple math XD I was up 'till 6am studying for an engineering statics midterm I had today. But you are correct!

$\large (e^{2t}y)'=\frac{ 2 }{ 5 }e^{t}$
Don't forget the $+C$! :)

anonymous · Answer

Thanks for your time!!

anonymous · Answer

You are most certainly welcome! X)