y^{'''}-16y^'=te^{-4t}+5cos(4t)

Lösung

y^{^{'''}} - 16 y^{^{'}} = t e^{- 4 t} + 5 cos (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} - 80 sin ( 4 t )}{2048}

Schritte zur Lösung

y^{'''} (t) - 16 y^{'} (t) = t e^{- 4 t} + 5 cos (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} - 80 sin ( 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} - 80 sin ( 4 t )}{2048}

y^{^{''}} - y^{^{'}} = 4 cos (2 x), y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 2 y^{^{'}} + 2 y = e^{(- x)} \cdot cos (x)

y^{^{''}} + y - x = 0

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

y^{^{''}} + 3 y^{^{'}} = x^{2} + 9