x^'+3/200 x=0.006

解答

x^{^{'}} + \frac{3}{200} x = 0.006

x = - \frac{e ^{- 0.015 t - c_{1}}}{0.015} + \frac{0.006}{0.015}

求解步骤

x^{'} (t) + \frac{3}{200} x = 0.006

求解可分离方程:

x = - \frac{e ^{- 0.015 t - c_{1}}}{0.015} + \frac{0.006}{0.015}

x = - \frac{e ^{- 0.015 t - c_{1}}}{0.015} + \frac{0.006}{0.015}

y^{2} \cdot d x - x \cdot y \cdot d y = x^{2} \cdot y \cdot d y

\frac{d p}{d t} = \frac{t \cdot cos ( t ^{2} )}{p ^{2}}

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

\frac{d y}{d x} = \frac{y ^{2} - 1}{2}

y^{^{'}} e^{- x} = y^{2}