y^{''}-6y^'+5y=sin(4x),y(0)=1,y^'(0)=-4

解

y^{^{''}} - 6 y^{^{'}} + 5 y = sin (4 x), y (0) = 1, y^{^{'}} (0) = - 4

y = (- \frac{149}{68} + \frac{673}{697}) e^{5 x} + \frac{149}{68} e^{x} - \frac{11}{697} sin (4 x) + \frac{24}{697} cos (4 x)

解答ステップ

y^{''} (x) - 6 y^{'} (x) + 5 y = sin (4 x)

線形 ODE を解く:

y = (- \frac{149}{68} + \frac{673}{697}) e^{5 x} + \frac{149}{68} e^{x} - \frac{11}{697} sin (4 x) + \frac{24}{697} cos (4 x)

y = (- \frac{149}{68} + \frac{673}{697}) e^{5 x} + \frac{149}{68} e^{x} - \frac{11}{697} sin (4 x) + \frac{24}{697} cos (4 x)