y^{''}-64y=sinh(8x)

Lösung

y^{^{''}} - 64 y = sinh (8 x)

y = c_{1} e^{8 x} + c_{2} e^{- 8 x} + \frac{16 e ^{8 x} x + 16 e ^{- 8 x} x - 8 sinh ( 8 x ) - e ^{- 8 x} + e ^{8 x}}{512}

Schritte zur Lösung

y^{''} (x) - 64 y = sinh (8 x)

Solve linear ODE:

y = c_{1} e^{8 x} + c_{2} e^{- 8 x} + \frac{16 e ^{8 x} x + 16 e ^{- 8 x} x - 8 sinh ( 8 x ) - e ^{- 8 x} + e ^{8 x}}{512}

y = c_{1} e^{8 x} + c_{2} e^{- 8 x} + \frac{16 e ^{8 x} x + 16 e ^{- 8 x} x - 8 sinh ( 8 x ) - e ^{- 8 x} + e ^{8 x}}{512}

y^{^{''}} - y^{^{'}} - 2 y = - 2 x^{3} + x^{2} + 4 x + 1

y^{^{''}} - 4 y^{^{'}} + 3 y = x e^{2 x}

y^{^{''}} + 4 y = 3 sin (x) + 5 cos (3 x)

y^{^{''}} + 4 y = x sin^{2} (x)

y^{^{''}} - 2 y^{^{'}} - 3 y = 4, y (0) = 1, y^{^{'}} (0) = - 1