y^{''}-25y=sinh(5x)

Lösung

y^{^{''}} - 25 y = sinh (5 x)

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} + \frac{10 e ^{5 x} x + 10 e ^{- 5 x} x - 8 sinh ( 5 x ) - e ^{- 5 x} + e ^{5 x}}{200}

Schritte zur Lösung

y^{''} (x) - 25 y = sinh (5 x)

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} + \frac{10 e ^{5 x} x + 10 e ^{- 5 x} x - 8 sinh ( 5 x ) - e ^{- 5 x} + e ^{5 x}}{200}

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} + \frac{10 e ^{5 x} x + 10 e ^{- 5 x} x - 8 sinh ( 5 x ) - e ^{- 5 x} + e ^{5 x}}{200}

y^{^{''}} + y^{^{'}} - 12 y = e^{x} + e^{2 x} - 1

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

y^{^{''}} - y^{^{'}} = e^{2 x}, y (0) = 0, y (1) = 0

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

y^{^{''}} - 2 y^{^{'}} + 5 y = 2 x^{2} + 12