ay^{''}+by^'+cy=g(t)

Lösung

a y^{^{''}} + b y^{^{'}} + cy = g (t)

y = c_{1} e^{\frac{t ( - b + b ^{2} - 4 c a )}{2 a}} + c_{2} e^{\frac{t ( - b - b ^{2} - 4 c a )}{2 a}} + \frac{g t}{c} - \frac{g b}{c ^{2}}

Schritte zur Lösung

a y^{''} (t) + b y^{'} (t) + cy = g (t)

Solve linear ODE:

y = c_{1} e^{\frac{t ( - b + b ^{2} - 4 c a )}{2 a}} + c_{2} e^{\frac{t ( - b - b ^{2} - 4 c a )}{2 a}} + \frac{g t}{c} - \frac{g b}{c ^{2}}

y = c_{1} e^{\frac{t ( - b + b ^{2} - 4 c a )}{2 a}} + c_{2} e^{\frac{t ( - b - b ^{2} - 4 c a )}{2 a}} + \frac{g t}{c} - \frac{g b}{c ^{2}}

(d^{2} - 4) y = 2 x

y^{^{''}} + y^{^{'}} - 2 y = 2 t - 40 cos (2 t)

y^{^{''}} - 6 y^{^{'}} + 45 y = - 4 sin (2 t)

y^{^{''}} + 16 y = sin (x)

x^{^{''}} + 36 x = 100 cos (4 t)