(d^2y)/(dt^2)-y=e^t

Lösung

\frac{d ^{2} y}{d t ^{2}} - y = e^{t}

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

Schritte zur Lösung

\frac{d ^{2} y}{d t ^{2}} - y = e^{t}

Solve linear ODE:

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

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

x^{^{''}} - 5 x^{^{'}} + 4 x = 8 e^{t}

y^{^{''}} + 9 y = 10 e^{- t}

y^{^{''}} + 3 y^{^{'}} - 4 y = cos (2 x)

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = e^{x}

y^{^{''}} - y = 8