Math Solutions

(Step-by-Step) Find the first 7 nonzero terms of the Maclaurin series of the general solution of the differential equation y^prime \prime-e^x y^prime+2 y=1

Question: Find the first 7 nonzero terms of the Maclaurin series of the general solution of the differential equation

\[y^{\prime \prime}-e^{x} y^{\prime}+2 y=1\]

Also find the recurrence relation for the coefficients in the series solution. Hint: Consider rewriting the double sum using the Cauchy product.

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