y^{''}-4y^'+3y=3te^t,y(0)=1,y^'(0)=-5

Lösung

y^{^{''}} - 4 y^{^{'}} + 3 y = 3 t e^{t}, y (0) = 1, y^{^{'}} (0) = - 5

y = (1 - \frac{29}{8}) e^{3 t} + \frac{29}{8} e^{t} - \frac{3 e ^{t} t ^{2}}{4} - \frac{3 e ^{t} t}{4}

Schritte zur Lösung

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

Solve linear ODE:

y = (1 - \frac{29}{8}) e^{3 t} + \frac{29}{8} e^{t} - \frac{3 e ^{t} t ^{2}}{4} - \frac{3 e ^{t} t}{4}

y = (1 - \frac{29}{8}) e^{3 t} + \frac{29}{8} e^{t} - \frac{3 e ^{t} t ^{2}}{4} - \frac{3 e ^{t} t}{4}

y^{^{''}} - 3 y^{^{'}} - 4 y = 8 e^{x} cos (2 x)

y^{^{''}} + 6 y^{^{'}} + 5 y = - 1020 sin (3 t)

(D^{2} + 4 D + 8) y = 4 sin (2 x)

y^{^{''}} + 9 y = 2 t^{2} - 2, y (0) = 0, y^{^{'}} (0) = - 8

y^{^{'''}} + 3 y^{^{''}} - y^{^{'}} - 3 y = 3 x - 14