(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find a general solution to [tex]\frac{d^2x}{dt^2}-2\frac{dx}{dt}=1-4t+e^t[/tex]

2. Relevant equations

None really.

3. The attempt at a solution

I know that a complimentary solution is [tex]x=c_1+c_2e^{2t}[/tex]

But when I try to guess say: [tex]x_p=At+B+Ce^t[/tex] and plug into the DE, I do not get anything to equate to 4t. Do I have to guess a degree higher? And if so, do I include all coefficients such that my guess becomes [tex]x_p=At^2+Bt+C+De^t[/tex]?

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# Homework Help: Second Order Non-homogeneous Constant Coefficient Differential Equation

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