y^{''}-2y^'+y=30e^tt^{-7}

Lösung

y^{^{''}} - 2 y^{^{'}} + y = 30 e^{t} t^{- 7}

y = c_{1} e^{t} + c_{2} t e^{t} + \frac{e ^{t}}{t ^{5}}

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) + y = 30 e^{t} t^{- 7}

Solve linear ODE:

y = c_{1} e^{t} + c_{2} t e^{t} + \frac{e ^{t}}{t ^{5}}

y = c_{1} e^{t} + c_{2} t e^{t} + \frac{e ^{t}}{t ^{5}}

y^{^{''}} + 4 y = 12 t

y^{^{''}} - y^{^{'}} + 2 y = 2 e^{2 t} + 5 t - 1

y^{^{''}} + y^{^{'}} + y = k

4 y^{^{''}} - y = e^{\frac{1}{2} x} + 7

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