y^{''}-2y^'+y= t/(e^t)+(e^t)/t

Lösung

y^{^{''}} - 2 y^{^{'}} + y = \frac{t}{e ^{t}} + \frac{e ^{t}}{t}

y = c_{1} e^{t} + c_{2} t e^{t} + \frac{1}{4} e^{- t} t - e^{t} t + e^{t} t ln (t) + \frac{1}{4} e^{- t}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{t} + c_{2} t e^{t} + \frac{1}{4} e^{- t} t - e^{t} t + e^{t} t ln (t) + \frac{1}{4} e^{- t}

y = c_{1} e^{t} + c_{2} t e^{t} + \frac{1}{4} e^{- t} t - e^{t} t + e^{t} t ln (t) + \frac{1}{4} e^{- t}

4 y^{^{''}} - 7 y^{^{'}} + 3 y = t e^{2 t} sin (- 2 t)

(D^{2} - 3 D + 2) y = e^{5 x}

y^{^{''''}} - 2 y^{^{'''}} + y^{^{''}} = e^{x + 1}

y^{^{''}} + 3 y^{^{'}} + 6 = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = 1, y^{^{'}} (0) = 0