# Toronto Math Forum

## MAT244--2018F => MAT244--Lectures & Home Assignments => Topic started by: Yunqi(Yuki) Huang on October 10, 2018, 01:36:33 AM

Title: non-homogenous equation
Post by: Yunqi(Yuki) Huang on October 10, 2018, 01:36:33 AM
I wonder that how can we solve the problem when the right-hand side of the non-homogenous equation is only a constant?
Title: Re: non-homogenous equation
Post by: Victor Ivrii on October 10, 2018, 04:05:48 AM
What equation?Linear? With constant coefficients? Read a textbook or follpw lectures
Title: Re: non-homogenous equation
Post by: Yunqi(Yuki) Huang on October 10, 2018, 10:25:45 AM
I mean we usually solve the second order equation like y''+2y'+y= 2e^(-t), which right-hand side is a non-homogenous equation. We could assume right-hand side is Y(t)=Ae^(-t), then substitute y'' and y' and y in the ordinary equation. However, how can we solve the equation like y''+2y'+y=3? If it is right to assume Y(t)=A for the right-hand side?
Title: Re: non-homogenous equation
Post by: Wei Cui on October 10, 2018, 10:45:38 AM
If the equation is a non-homogeneous and the right-hand side is a constant, I think you can assume that the particular solution $y(t) = at + b$ and try to solve the equation.
Title: Re: non-homogenous equation
Post by: Victor Ivrii on October 10, 2018, 01:43:59 PM
I mean we usually solve the second order equation like y''+2y'+y= 2e^(-t), which right-hand side is a non-homogenous equation. We could assume right-hand side is Y(t)=Ae^(-t), then substitute y'' and y' and y in the ordinary equation. However, how can we solve the equation like y''+2y'+y=3? If it is right to assume Y(t)=A for the right-hand side?
YES, because $3=3e^{0x}$ and $r=0$ is not a characteristic root.