Consider the differential equation
y′′+αy′+βy=t+e^(4t).

Suppose the form of the particular solution to this differential equation as prescribed by the method of undetermined coefficients is

yp(t)=A1t^2+A0t+B0te^(4t).

Determine the constants α and β.

I found out that β = 0. I don't know how to proceed to get α

Question

Consider the differential equation
y′′+αy′+βy=t+e^(4t).

Suppose the form of the particular solution to this differential equation as prescribed by the method of undetermined coefficients is

yp(t)=A1t^2+A0t+B0te^(4t).

Determine the constants α and β. 

I found out that β = 0. I don't know how to proceed to get α

mrhoola · Answer

http://tutorial.math.lamar.edu/Classes/DE/UndeterminedCoefficients.aspx

anonymous · Answer

because C=constant should be homogenious solution.

mrhoola · Answer

that might help

anonymous · Answer

so beta=0

anonymous · Answer

if beta#0 so you should build yp=at2+bt+c+de4t+...

anonymous · Answer

because in your yp there is no c as a constant so it must be homogenious solution or beta=0.  Is it clear ?

anonymous · Answer

Not really... I already know that beta = 0. How do go about finding alpha?