x^{''}-2x^'+x=1t^2e^t

Lösung

x^{^{''}} - 2 x^{^{'}} + x = 1 t^{2} e^{t}

x = c_{1} e^{t} + c_{2} t e^{t} + \frac{e ^{t} t ^{4}}{12}

Schritte zur Lösung

x^{''} (t) - 2 x^{'} (t) + x = 1 t^{2} e^{t}

Solve linear ODE:

x = c_{1} e^{t} + c_{2} t e^{t} + \frac{e ^{t} t ^{4}}{12}

x = c_{1} e^{t} + c_{2} t e^{t} + \frac{e ^{t} t ^{4}}{12}

y^{^{''}} - 4 y^{^{'}} + 4 y = 8 x^{2} e^{2 x} sin (2 x)

y^{^{''}} - 2 y^{^{'}} - 8 y = - 2 e^{2 x} - 5 x e^{- 4 x} - 2 x

y^{^{''}} - 16 y = 48 t - 24 e^{- 4 t}, y (0) = 0, y^{^{'}} (0) = 16

y^{^{''}} - 8 y^{^{'}} + 16 y = 8 x + 4

y^{^{''}} + 6 y^{^{'}} - 7 y = 3 e^{2 x} - 2 e^{3 x}