(d^2y)/(dt^2)+2*(dy)/(dt)+2y=11t^3

Lösung

\frac{d ^{2} y}{d t ^{2}} + 2 \cdot \frac{d y}{d t} + 2 y = 11 t^{3}

y = e^{- t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{11 t ^{3}}{2} - \frac{33 t ^{2}}{2} + \frac{33 t}{2}

Schritte zur Lösung

\frac{d ^{2} y}{d t ^{2}} + 2 \cdot \frac{d y}{d t} + 2 y = 11 t^{3}

Solve linear ODE:

y = e^{- t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{11 t ^{3}}{2} - \frac{33 t ^{2}}{2} + \frac{33 t}{2}

y = e^{- t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{11 t ^{3}}{2} - \frac{33 t ^{2}}{2} + \frac{33 t}{2}

3 y^{^{''}} + 27 y^{^{'}} + 42 y = 25 sin (t)

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

y^{^{''}} - 9 y^{^{'}} + 8 y = x

y^{^{''}} + 14 y^{^{'}} + 50 y = 371 cos (t)

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