y^{''}-3y^'-10y=-4e^{4t},y(0)=0,y^'(0)=0

解

y^{^{''}} - 3 y^{^{'}} - 10 y = - 4 e^{4 t}, y (0) = 0, y^{^{'}} (0) = 0

y = (\frac{2}{21} - \frac{2}{3}) e^{5 t} - \frac{2}{21} e^{- 2 t} + \frac{2}{3} e^{4 t}

解答ステップ

y^{''} (t) - 3 y^{'} (t) - 10 y = - 4 e^{4 t}

線形 ODE を解く:

y = (\frac{2}{21} - \frac{2}{3}) e^{5 t} - \frac{2}{21} e^{- 2 t} + \frac{2}{3} e^{4 t}

y = (\frac{2}{21} - \frac{2}{3}) e^{5 t} - \frac{2}{21} e^{- 2 t} + \frac{2}{3} e^{4 t}