y^'=((xy+3y))/(x-3)

解答

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

y = e^{x + c_{1}} x^{6} - 18 e^{x + c_{1}} x^{5} + 135 e^{x + c_{1}} x^{4} - 540 e^{x + c_{1}} x^{3} + 1215 e^{x + c_{1}} x^{2} - 1458 e^{x + c_{1}} x + 729 e^{x + c_{1}}

求解步骤

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

求解可分离方程:

y = e^{x + c_{1}} x^{6} - 18 e^{x + c_{1}} x^{5} + 135 e^{x + c_{1}} x^{4} - 540 e^{x + c_{1}} x^{3} + 1215 e^{x + c_{1}} x^{2} - 1458 e^{x + c_{1}} x + 729 e^{x + c_{1}}

y = e^{x + c_{1}} x^{6} - 18 e^{x + c_{1}} x^{5} + 135 e^{x + c_{1}} x^{4} - 540 e^{x + c_{1}} x^{3} + 1215 e^{x + c_{1}} x^{2} - 1458 e^{x + c_{1}} x + 729 e^{x + c_{1}}

\frac{d}{d x} (ln (y)) = \frac{1}{3} ln (x^{2} - 9)

y^{^{'}} = sin (x) sin (y)

\frac{d Q}{d x} = 5 x^{4} Q

\frac{d v}{d t} = 10 + 2 v

y^{^{'}} = y^{- 9} x^{9}, y (0) = 9