y^{''}-y^'-2y=sin(3t),y(0)=1,y(0)=-1

Lösung

y^{^{''}} - y^{^{'}} - 2 y = sin (3 t), y (0) = 1, y (0) = - 1

y = (- c_{2} + \frac{127}{130}) e^{2 t} + c_{2} e^{- t} - \frac{11}{130} sin (3 t) + \frac{3}{130} cos (3 t)

Schritte zur Lösung

y^{''} (t) - y^{'} (t) - 2 y = sin (3 t)

Solve linear ODE:

y = (- c_{2} + \frac{127}{130}) e^{2 t} + c_{2} e^{- t} - \frac{11}{130} sin (3 t) + \frac{3}{130} cos (3 t)

y = (- c_{2} + \frac{127}{130}) e^{2 t} + c_{2} e^{- t} - \frac{11}{130} sin (3 t) + \frac{3}{130} cos (3 t)

y^{^{''}} + 6 y^{^{'}} + 9 y = t^{2} \cdot e^{- 3 t}

3 y^{^{''}} + 75 y = 10 cos (5 t)

y^{^{''''}} - y = 8 e^{x}

y^{^{''}} + y = t, y (0) = 4, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 3 y^{^{'}} - 2 y = 2 t^{2} + 4 t + 4