Toronto Math Forum
MAT2442018F => MAT244Lectures & Home Assignments => Topic started by: Yunqi(Yuki) Huang on October 10, 2018, 01:36:33 AM

I wonder that how can we solve the problem when the righthand side of the nonhomogenous equation is only a constant?

What equation?Linear? With constant coefficients? Read a textbook or follpw lectures

I mean we usually solve the second order equation like y''+2y'+y= 2e^(t), which righthand side is a nonhomogenous equation. We could assume righthand 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 righthand side?

If the equation is a nonhomogeneous and the righthand side is a constant, I think you can assume that the particular solution $y(t) = at + b$ and try to solve the equation.

I mean we usually solve the second order equation like y''+2y'+y= 2e^(t), which righthand side is a nonhomogenous equation. We could assume righthand 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 righthand side?
YES, because $3=3e^{0x}$ and $r=0$ is not a characteristic root.