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

Lösung

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

y = c_{1} e^{8 x} + c_{2} e^{- 8 x} + \frac{e ^{8 x} ( - 4 e ^{- 8 x} cosh ( 8 x ) - 4 e ^{- 8 x} sinh ( 8 x ) - e ^{- 16 x} + 16 x ) - e ^{- 8 x} ( 16 x + e ^{16 x} )}{512}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{8 x} + c_{2} e^{- 8 x} + \frac{e ^{8 x} ( - 4 e ^{- 8 x} cosh ( 8 x ) - 4 e ^{- 8 x} sinh ( 8 x ) - e ^{- 16 x} + 16 x ) - e ^{- 8 x} ( 16 x + e ^{16 x} )}{512}

y = c_{1} e^{8 x} + c_{2} e^{- 8 x} + \frac{e ^{8 x} ( - 4 e ^{- 8 x} cosh ( 8 x ) - 4 e ^{- 8 x} sinh ( 8 x ) - e ^{- 16 x} + 16 x ) - e ^{- 8 x} ( 16 x + e ^{16 x} )}{512}

y^{^{''}} - 2 y^{^{'}} + y = \frac{5 e ^{t}}{1 + t ^{2}}

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

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

4 y^{^{''}} - 4 y^{^{'}} + y = 16 e^{\frac{x}{2}}

y^{^{''}} - y^{^{'}} = e^{x} sin (x)