y^'=(5y)/(x+3)

解答

y^{^{'}} = \frac{5 y}{x + 3}

y = e^{c_{1}} x^{5} + 15 e^{c_{1}} x^{4} + 90 e^{c_{1}} x^{3} + 270 e^{c_{1}} x^{2} + 405 e^{c_{1}} x + 243 e^{c_{1}}

求解步骤

y^{'} (x) = \frac{5 y}{x + 3}

求解可分离方程:

y = e^{c_{1}} x^{5} + 15 e^{c_{1}} x^{4} + 90 e^{c_{1}} x^{3} + 270 e^{c_{1}} x^{2} + 405 e^{c_{1}} x + 243 e^{c_{1}}

y = e^{c_{1}} x^{5} + 15 e^{c_{1}} x^{4} + 90 e^{c_{1}} x^{3} + 270 e^{c_{1}} x^{2} + 405 e^{c_{1}} x + 243 e^{c_{1}}

x \to - 7 lim (\frac{x ^{2} - 2}{7 - x})

\int (4 x - 1)^{2} d x

in v erse l a pl a ce \frac{1}{s ^{2} ( s + 2 )}

\frac{d}{d x} ((lo g_{10} (x))^{2})

y^{^{''}} + 3 y = 5