y^{''}+4y=3cos(at)

Lösung

y^{^{''}} + 4 y = 3 cos (a t)

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{3 cos ( a t )}{- a ^{2} + 4}

Schritte zur Lösung

y^{''} (t) + 4 y = 3 cos (a t)

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{3 cos ( a t )}{- a ^{2} + 4}

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{3 cos ( a t )}{- a ^{2} + 4}

y^{^{'''}} + 9 y^{^{''}} + 27 y^{^{'}} + 27 y = 7 e^{- 3 x}

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} = 2 x^{2} - x + 1

y^{^{''}} + 36 y = 24 sin (6 x)

y^{^{''''}} - 4 y^{^{'''}} + 6 y^{^{''}} - 4 y^{^{'}} + y = e^{x}

2 x^{^{''}} + 5 x^{^{'}} + 2 x = 2 e - 2 t - t