Author Topic: non-homogenous equation  (Read 917 times)

Yunqi(Yuki) Huang

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non-homogenous equation
« 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?

Victor Ivrii

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Re: non-homogenous equation
« Reply #1 on: October 10, 2018, 04:05:48 AM »
What equation?Linear? With constant coefficients? Read a textbook or follpw lectures

Yunqi(Yuki) Huang

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Re: non-homogenous equation
« Reply #2 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?

Wei Cui

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Re: non-homogenous equation
« Reply #3 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.

Victor Ivrii

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Re: non-homogenous equation
« Reply #4 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.