(dv)/(dt)=0.4-1/30 v

解答

\frac{d v}{d t} = 0.4 - \frac{1}{30} v

v = - \frac{e ^{\frac{- t - c _{1}}{30}}}{0.03333 \dots} + \frac{0.4}{0.03333 \dots}

求解步骤

\frac{d v}{d t} = 0.4 - \frac{1}{30} v

求解可分离方程:

v = - \frac{e ^{\frac{- t - c _{1}}{30}}}{0.03333 \dots} + \frac{0.4}{0.03333 \dots}

v = - \frac{e ^{\frac{- t - c _{1}}{30}}}{0.03333 \dots} + \frac{0.4}{0.03333 \dots}

y^{^{'}} + 9 x y = 8 x, y (0) = 4

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

x y^{^{'}} = y^{2} ln (x)

(x^{3} y^{3}) d x - 3 x y^{2} d y = 0

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