x^{''}-x=4e^t

Lösung

x^{^{''}} - x = 4 e^{t}

x = c_{1} e^{t} + c_{2} e^{- t} + 2 t e^{t}

Schritte zur Lösung

x^{''} (t) - x = 4 e^{t}

Solve linear ODE:

x = c_{1} e^{t} + c_{2} e^{- t} + 2 t e^{t}

x = c_{1} e^{t} + c_{2} e^{- t} + 2 t e^{t}

y^{^{''}} + y^{^{'}} - 2 y = x^{2} + 3

y^{^{'''}} + y^{^{'}} = e^{x}, y (0) = 0

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

d^{2} (d + 3)^{2} y = 9 e^{- 3 x}

y^{^{''}} - 11 y = e^{x}