x^{''}+ax=b

Lösung

x^{^{''}} + a x = b

x = c_{1} cos (a t) + c_{2} sin (a t) + \frac{b}{a}

Schritte zur Lösung

x^{''} (t) + a x = b

Solve linear ODE:

x = c_{1} cos (a t) + c_{2} sin (a t) + \frac{b}{a}

x = c_{1} cos (a t) + c_{2} sin (a t) + \frac{b}{a}

y^{^{''}} + 6 y^{^{'}} + 9 y = 12 e^{t}

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 1, y (0) = 0, y^{^{'}} (0) = 0

D (x) = 82.5 - 2 \cdot 5 x

y^{^{''}} + 6 y = 8 t

y^{^{''}} - y^{^{'}} - 6 y = 12 cos (3 x)