(d^2y)/(dt^2)+12(dy)/(dt)+32=32\H(t)

解

\frac{d ^{2} y}{d t ^{2}} + 12 \frac{d y}{d t} + 32 = 32 H (t)

y = c_{1} + c_{2} e^{- 12 t} + \int \frac{8 ( H ( t ) - 1 )}{3} d t + e^{- 12 t} \cdot \int - \frac{8 ( H ( t ) - 1 )}{3 e ^{- 12 t}} d t

解答ステップ

\frac{d ^{2} y}{d t ^{2}} + 12 \frac{d y}{d t} + 32 = 32 H (t)

線形 ODE を解く:

y = c_{1} + c_{2} e^{- 12 t} + \int \frac{8 ( H ( t ) - 1 )}{3} d t + e^{- 12 t} \cdot \int - \frac{8 ( H ( t ) - 1 )}{3 e ^{- 12 t}} d t

y = c_{1} + c_{2} e^{- 12 t} + \int \frac{8 ( H ( t ) - 1 )}{3} d t + e^{- 12 t} \cdot \int - \frac{8 ( H ( t ) - 1 )}{3 e ^{- 12 t}} d t