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Mathematics
Differential Equations
Solving an ODE with power series
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[QUOTE="HallsofIvy, post: 6271328, member: 637751"] Actually you have a many powers of x hidden in each sum. Also, though all your sums start at r= 0, in the first sum you have coefficients r and r- 1 so the first two terms are 0, It would be better to write it as [itex]\sum_{r= 2}^\infty a_r r(r-1)x^{r- 2}[/itex]. In order to get [itex]x^i[/itex], let i= r- 2 so that r= i+ 2 and the sum becomes [itex]\sum_{i= 0}^\infty a_{i+2}(i+2)(i+1)x^{i}[/itex]. Do the same with each of the other sums so that you have [itex]x^i[/itex] in each sum and can combine coefficients of "like powers". [/QUOTE]
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Solving an ODE with power series
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