I'm doing a initial value problem and need to use the method of undetermined coefficients. I have on the right side 2+2^x, and I'm unsure what guess I would use for this. I've seen every possible circumstance except for this case. For example, for e^3x, I would use Ae^3x. But what about 2+2^x?
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Remember $a^x=e^{\ln(a) x}$ so it is really the same case as $e^{cx}$. – Ian Mar 03 '21 at 22:22
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the ODE is 2u_(k+1) - 7u_k + 3u_(k-1) = 2 + 2^k – user14336952 Mar 03 '21 at 22:37
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1So we're not actually talking about an ODE ("Ordinary Differential Equation"), we're talking about a recurrence relation. Note that $2^x=e^{x\log2}$. – Gerry Myerson Mar 03 '21 at 22:58
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Did that help? Do you see how to do it now? – Gerry Myerson Mar 05 '21 at 12:04
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Are you still here? – Gerry Myerson Mar 07 '21 at 11:54