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The technique works for equations of any order for example first order If is a solution of the differential equation y 5x 4 y 0
The technique works for equations of any order for example first order If is a solution of the differential equation y 5x 4 y 0 then its coefficients a satisfy the following recurrence relation For k 0 ak 2 0 We also have y 1 a1 0 ao help numbers Therefore write the first few terms of a solution where y 0 1 9 2 81 40 x ak 1 0 y akak k 0 2 916 8 help numbers x x ak help formulas
The technique works for equations of any order for example first order If is a solution of the differential equation y 5x 4 y 0 then its coefficients a satisfy the following recurrence relation For k 0 ak 2 0 We also have y 1 a1 0 ao help numbers Therefore write the first few terms of a solution where y 0 1 9 2 81 40 x ak 1 0 y akak k 0 2 916 8 help numbers x x ak help formulas
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