Here's the question you clicked on:
haganmc
find particular solution to 2x' + x=3t^2
what methods do you know of?
undetermined coefficients
got a lousy connection i believe
happening to me too, OS is bugged today.
site is slow for me too :(
well, lets start by dividing off that 2 x' + x/2 = 3t^2/2 we want to determine an e^rt that will allow us to turn this into a product rule; e^t/2 should work e^(t/2) x' +e^(t/2) x/2 = e^(t/2)3t^2/2 when we integrate both sides we get \[e^{t/2}x= \int e^{t/2}\frac{3t^2}{2}dt\]
trial soln. is at^2 + bt +c 2x' = 4at + 2b x= at^2 +bt +c a=3 4a+b =0 2b+c =0 b=-12 c=24
\[\int e^{t/2}\frac{3t^2}{2}dt\] e^(t/2) +t^2 2e^(t/2) -2t 4e^(t/2) +2 8e^(t/2) \[2*\frac32e^{t/2}(t^2-4t+8)\]
forgot the +C at the end:) this gives us \[e^{t/2}x=3e^{t/2}(t^2-4t+8)+C\] divide off the e^{t/2} \[x=3(t^2-4t+8)+Ce^{-t/2}\]
my idea was undetermined coeffs tho was it
*wasnt .... ugh, when things slow down, they sloowww down
I did it the 'integrating factor' way too, just because I was curious... fair bit of work doing that integral..