y^{'''}-16y^'=te^{4t}

Lösung

y^{^{'''}} - 16 y^{^{'}} = t e^{4 t}

y = c_{1} + c_{2} e^{- 4 t} + c_{3} e^{4 t} + \frac{32 e ^{4 t} t ^{2} - 24 e ^{4 t} t + 7 e ^{4 t}}{2048}

Schritte zur Lösung

y^{'''} (t) - 16 y^{'} (t) = t e^{4 t}

Solve linear ODE:

y = c_{1} + c_{2} e^{- 4 t} + c_{3} e^{4 t} + \frac{32 e ^{4 t} t ^{2} - 24 e ^{4 t} t + 7 e ^{4 t}}{2048}

y = c_{1} + c_{2} e^{- 4 t} + c_{3} e^{4 t} + \frac{32 e ^{4 t} t ^{2} - 24 e ^{4 t} t + 7 e ^{4 t}}{2048}

y^{^{''}} + 4 y = 8 t

y^{^{''}} + 4 y^{^{'}} + 6 y = 1 + e^{- 1}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} + y = 11 e^{x}

y^{^{''}} + 4 y = 9 t, y^{^{'}} (0) = 7

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