(dx)/(dt)+cos(t)x-cos(t)=0

解答

\frac{d x}{d t} + cos (t) x - cos (t) = 0

x = e^{- s i n (t) + c_{1}} + 1

求解步骤

\frac{d x}{d t} + cos (t) x - cos (t) = 0

求解可分离方程:

x = e^{- s i n (t) + c_{1}} + 1

x = e^{- s i n (t) + c_{1}} + 1

y^{^{'}} = y (1 - \frac{y}{2000})

\frac{d x}{d t} = 12 - \frac{36 x}{100}

\frac{d y}{d t} = - \frac{1}{50} (y - 17)

\frac{d}{d t} (45440 x) = - 28920 x

\frac{d y}{d x} = - \frac{3}{8} x^{3} y^{7}