y^{''}-16y=sinh(4x)

Lösung

y^{^{''}} - 16 y = sinh (4 x)

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} + \frac{8 e ^{4 x} x + 8 e ^{- 4 x} x - 8 sinh ( 4 x ) - e ^{- 4 x} + e ^{4 x}}{128}

Schritte zur Lösung

y^{''} (x) - 16 y = sinh (4 x)

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} + \frac{8 e ^{4 x} x + 8 e ^{- 4 x} x - 8 sinh ( 4 x ) - e ^{- 4 x} + e ^{4 x}}{128}

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} + \frac{8 e ^{4 x} x + 8 e ^{- 4 x} x - 8 sinh ( 4 x ) - e ^{- 4 x} + e ^{4 x}}{128}

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

x^{^{''}} + 4 x = sin^{2} (2 t)

y^{^{''}} + 3 y^{^{'}} + 6 y = 4 e^{- 3 t} sin (t)

y^{^{'''}} - 2 y^{^{''}} - y^{^{'}} + 2 y = e^{5 t}

y^{^{''}} + 9 y^{^{'}} + 8 y = e^{2 t}