ODE No. 1583

2.1583 ODE No. 1583

$a y^{(n - 1)} (x) - f (x) + y^{(n)} (x) = 0$ ✓ Mathematica : cpu = 95.2137 (sec), leaf count = 120

${{y (x) \to (Integrate \overset{`}{} $ $ a $ 133499 - 1) (Integrate \overset{`}{} $ $ a $ 133502 - 1) (\frac{x^{2}}{2} - x) e^{- a Integrate \overset{`}{} $ $ a $ 180050} (Integrate [e^{a K [1]} f (K [1]), {K [1], 1, Integrate \overset{`}{} $ $ a $ 180050}, Assumptions \to (Integrate \overset{`}{} $ $ a $ 133499 \notin R \lor (1 < ℜ (Integrate \overset{`}{} $ $ a $ 133502) < Integrate \overset{`}{} $ $ a $ 133499 \land ℑ (Integrate \overset{`}{} $ $ a $ 133502) = 0) \lor (ℜ (Integrate \overset{`}{} $ $ a $ 133499) < Integrate \overset{`}{} $ $ a $ 133502 < 1 \land ℑ (Integrate \overset{`}{} $ $ a $ 133499) = 0)) \land (ℑ (x) \neq 0 \lor 1 < Integrate \overset{`}{} $ $ a $ 133499 < x \lor x < Integrate \overset{`}{} $ $ a $ 133499 < 1) \land (ℑ (Integrate \overset{`}{} $ $ a $ 133502) \neq 0 \lor 1 < Integrate \overset{`}{} $ $ a $ 180050 < Integrate \overset{`}{} $ $ a $ 133502 \lor Integrate \overset{`}{} $ $ a $ 133502 < Integrate \overset{`}{} $ $ a $ 180050 < 1)] + c_{1}) + c_{5} x^{3} + c_{4} x^{2} + c_{3} x + c_{2}}}$

✓ Maple : cpu = 0.03 (sec), leaf count = 40

${y (x) = \frac{e^{- a x}_C 1}{a^{4}} + \frac{f x^{4}}{24 a} + \frac{x^{3}_C 2}{6} + \frac{_C 3 x^{2}}{2} +_C 4 x +_C 5}$

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