(dq)/(dt)+1/(5*10^{-9)}q= 200/1000

解

\frac{d q}{d t} + \frac{1}{5 \cdot 1 0 ^{- 9}} q = \frac{200}{1000}

q = - \frac{e ^{- 200000000 t - c_{1}}}{1000000000} + \frac{1}{1000000000}

解答ステップ

\frac{d q}{d t} + \frac{1}{5 \cdot 1 0 ^{- 9}} q = \frac{200}{1000}

分離可能 ODE を解く:

q = - \frac{e ^{- 200000000 t - c_{1}}}{1000000000} + \frac{1}{1000000000}

q = - \frac{e ^{- 200000000 t - c_{1}}}{1000000000} + \frac{1}{1000000000}