y^{'''}-y^'=xe^{(-x)}+5cos(x)

Lösung

y^{^{'''}} - y^{^{'}} = x e^{(- x)} + 5 cos (x)

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} + \frac{2 e ^{- x} x ^{2} + 6 e ^{- x} x - 20 sin ( x ) + 7 e ^{- x}}{8}

Schritte zur Lösung

y^{'''} (x) - y^{'} (x) = x e^{(- x)} + 5 cos (x)

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} + \frac{2 e ^{- x} x ^{2} + 6 e ^{- x} x - 20 sin ( x ) + 7 e ^{- x}}{8}

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} + \frac{2 e ^{- x} x ^{2} + 6 e ^{- x} x - 20 sin ( x ) + 7 e ^{- x}}{8}

y^{^{'''}} - y = 1, y (0) = 0, y^{^{'}} (0) = 0, y^{^{''}} (0) = 0

y^{^{''}} + y^{^{'}} - 12 y = 12

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = x - 8 e x

y^{^{''}} - 36 y^{^{'}} = - 42 e^{- 5 t}, y (0) = 7, y^{^{'}} (0) = 0

2 \frac{d ^{2} y}{d t ^{2}} + 20 \frac{d y}{d t} + 50 = 8 \cdot (t)