xy^2(dy)/(dx)=x+6

解答

x y^{2} \frac{d y}{d x} = x + 6

y = 3 3 x + 18 ln (x) + c_{1}

求解步骤

x y^{2} \frac{d y}{d x} = x + 6

求解可分离方程:

y = 3 3 x + 18 ln (x) + c_{1}

y = 3 3 x + 18 ln (x) + c_{1}

\frac{d y}{d x} + 5 y = - 4

y^{^{'}} = \frac{- ( 3 y ^{2} + 1 ) x}{x ^{2} + 1}

\frac{d}{d x} (7 x^{2} + 8 ln (x y)) = 14

y^{^{'}} = \frac{4 x}{1 + 2 y}, y (2) = 0

y^{^{'}} = - \frac{9}{4} x^{6} y^{4}