x^{''}-6x^'+9x=e^{3t}

Lösung

x^{^{''}} - 6 x^{^{'}} + 9 x = e^{3 t}

x = c_{1} e^{3 t} + c_{2} t e^{3 t} + \frac{e ^{3 t} t ^{2}}{2}

Schritte zur Lösung

x^{''} (t) - 6 x^{'} (t) + 9 x = e^{3 t}

Solve linear ODE:

x = c_{1} e^{3 t} + c_{2} t e^{3 t} + \frac{e ^{3 t} t ^{2}}{2}

x = c_{1} e^{3 t} + c_{2} t e^{3 t} + \frac{e ^{3 t} t ^{2}}{2}

y^{^{''}} + 100 y^{^{'}} + 2500 y = 30, y (0) = 0, y^{^{'}} (0) = 2

l in e a r \frac{d ^{2} x}{d t ^{2}} + x = 6 cos (2 t), x (0) = 3

\frac{1}{2} y^{^{''}} + 2 y = 4 tan (2 t) - \frac{1}{2} e^{2 t}

y^{^{''}} + 4 y^{^{'}} + 4 y = 2 x + 6, y (0) = 1, y^{^{'}} (0) = \frac{1}{2}

y^{^{''}} + y = 2 e^{- x}