(8+x)y^'=5y

解答

(8 + x) y^{^{'}} = 5 y

y = 32768 e^{c_{1}} + 20480 e^{c_{1}} x + 5120 e^{c_{1}} x^{2} + 640 e^{c_{1}} x^{3} + 40 e^{c_{1}} x^{4} + e^{c_{1}} x^{5}

求解步骤

(8 + x) y^{'} (x) = 5 y

求解可分离方程:

y = 32768 e^{c_{1}} + 20480 e^{c_{1}} x + 5120 e^{c_{1}} x^{2} + 640 e^{c_{1}} x^{3} + 40 e^{c_{1}} x^{4} + e^{c_{1}} x^{5}

y = 32768 e^{c_{1}} + 20480 e^{c_{1}} x + 5120 e^{c_{1}} x^{2} + 640 e^{c_{1}} x^{3} + 40 e^{c_{1}} x^{4} + e^{c_{1}} x^{5}

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