y^{''}+3y^'+5y=sin(t),y(0)=1,y(0)=0

Lösung

y^{^{''}} + 3 y^{^{'}} + 5 y = sin (t), y (0) = 1, y (0) = 0

y = e^{- \frac{3 t}{2}} (\frac{28}{25} cos (\frac{11 t}{2}) + c_{2} sin (\frac{11 t}{2})) + \frac{4}{25} sin (t) - \frac{3}{25} cos (t)

Schritte zur Lösung

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

Solve linear ODE:

y = e^{- \frac{3 t}{2}} (\frac{28}{25} cos (\frac{11 t}{2}) + c_{2} sin (\frac{11 t}{2})) + \frac{4}{25} sin (t) - \frac{3}{25} cos (t)

y = e^{- \frac{3 t}{2}} (\frac{28}{25} cos (\frac{11 t}{2}) + c_{2} sin (\frac{11 t}{2})) + \frac{4}{25} sin (t) - \frac{3}{25} cos (t)

x^{^{''}} - 25 x = 3 e^{2 t}

(D^{3} + 3 D^{2} - 4) y = x e^{- 2 x}

y^{^{''}} - y = 1, y (0) = 0

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

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = e^{- t} + 14 t