y^{'''}+7y^{''}+8y^'-16y=-3e^x-2

Lösung

y^{^{'''}} + 7 y^{^{''}} + 8 y^{^{'}} - 16 y = - 3 e^{x} - 2

y = c_{1} e^{x} + c_{2} e^{- 4 x} + c_{3} x e^{- 4 x} - \frac{3 e ^{x} x}{25} + \frac{1}{8}

Schritte zur Lösung

y^{'''} (x) + 7 y^{''} (x) + 8 y^{'} (x) - 16 y = - 3 e^{x} - 2

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 4 x} + c_{3} x e^{- 4 x} - \frac{3 e ^{x} x}{25} + \frac{1}{8}

y = c_{1} e^{x} + c_{2} e^{- 4 x} + c_{3} x e^{- 4 x} - \frac{3 e ^{x} x}{25} + \frac{1}{8}

y^{^{''''}} + 2 y^{^{''}} + y = (x - 1)^{2}

y^{^{''}} + y^{^{'}} - 6 y = 2 t

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 8 + 2 sin (x)

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 2 y = 2 x

y^{^{''}} - 2 y^{^{'}} + y = \frac{11 e ^{t}}{1 + t ^{2}}