Thread: Ordinary 2nd Ordinary Non-homogenous DE

I wuould please like some verifcation on my work i think am on the write track, the question itself is

y''-4y=3e^(2x)+12x-2

For my homogeneous left side equation i have yh(x)=c1e^2x+c2e^-2x

My particular guess for the right side was: ae^2x + bx + c (and since e^2x appears both in the homo and the right side i multiply by x so i have )

axe^2x+bx+c as my guess doing the deritive and equating like terms i get,
a=4/3, b=-3,c=1/4
? am not sure if these are my correct coeffcients any help will be appreciated! thanks!

Originally Posted by zangestu888

I wuould please like some verifcation on my work i think am on the write track, the question itself is

y''-4y=3e^(2x)+12x-2

For my homogeneous left side equation i have yh(x)=c1e^2x+c2e^-2x

My particular guess for the right side was: ae^2x + bx + c (and since e^2x appears both in the homo and the right side i multiply by x so i have )

axe^2x+bx+c as my guess doing the deritive and equating like terms i get,
a=4/3, b=-3,c=1/4
? am not sure if these are my correct coeffcients any help will be appreciated! thanks!

Have you substituted your proposed solution into the differential equation to see if it works?

um yes i have a get a werid result thats why i posted the thread becuase i think thier might be some sort of error?

Originally Posted by zangestu888

I wuould please like some verifcation on my work i think am on the write track, the question itself is

y''-4y=3e^(2x)+12x-2

For my homogeneous left side equation i have yh(x)=c1e^2x+c2e^-2x

My particular guess for the right side was: ae^2x + bx + c (and since e^2x appears both in the homo and the right side i multiply by x so i have )

axe^2x+bx+c as my guess doing the deritive and equating like terms i get,
a=4/3, b=-3,c=1/4
? am not sure if these are my correct coeffcients any help will be appreciated! thanks!

Show HOW you got those numbers and we will try to help.

well i dereived my particular solution two times then subbed it into my differential equation when i equated terms i got those numbers but am not sure if my answr is correct i followed all procedures, am using method of undetermined coefficients

I did this..

yp(x)=axe^2x+bx+c i took the dervtive twice then i substtuted it into the de i got

(4ae^2x+4axe^2x)-4(axe^2x+bx+c)=r(x)
4ae^2x-4bx-4c=3e^2x+12x-2
a=3/4,b=-3,c=1/2

my final equation for the whole DE is...

y(x)=2e^x2+2e^-2x+3/4(x)e^2x-3x=1/2