y^{''}-9y=sinh(3x)

Lösung

y^{^{''}} - 9 y = sinh (3 x)

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} + \frac{6 e ^{3 x} x + 6 e ^{- 3 x} x - 8 sinh ( 3 x ) - e ^{- 3 x} + e ^{3 x}}{72}

Schritte zur Lösung

y^{''} (x) - 9 y = sinh (3 x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} + \frac{6 e ^{3 x} x + 6 e ^{- 3 x} x - 8 sinh ( 3 x ) - e ^{- 3 x} + e ^{3 x}}{72}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} + \frac{6 e ^{3 x} x + 6 e ^{- 3 x} x - 8 sinh ( 3 x ) - e ^{- 3 x} + e ^{3 x}}{72}

y^{^{''''}} - 2 y^{^{'''}} + y^{^{''}} = e^{x} + 1

y^{^{''}} + 6 y^{^{'}} - 7 y = 3 e^{2 x} - e^{- x}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} = tan (x)

y^{^{''}} - 2 y^{^{'}} - 3 y = 12 e^{x} - 6

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