(dp)/(dx)=k(a-p)

解答

\frac{d p}{d x} = k (a - p)

p = - e^{- k x - c_{1}} + a

求解步骤

\frac{d p}{d x} = k (a - p)

求解可分离方程:

p = - e^{- k x - c_{1}} + a

p = - e^{- k x - c_{1}} + a

(x^{2} - x) y^{^{'}} - (y^{2} + y) = 0

\frac{d y}{d x} = y x^{3} - x y

y^{^{'}} = 3 y, y (0) = 0

2 x y + 6 x + (x^{2} - 4) \frac{d y}{d x} = 0

\frac{d y}{d x} = \frac{x}{y}, y (0) = - 6