y^{'''}-y^{''}-25y^'+25y=4-e^x+e^{5x}

Lösung

y^{^{'''}} - y^{^{''}} - 25 y^{^{'}} + 25 y = 4 - e^{x} + e^{5 x}

y = c_{1} e^{x} + c_{2} e^{- 5 x} + c_{3} e^{5 x} + \frac{4}{25} + \frac{e ^{x} x}{24} + \frac{e ^{5 x} x}{40}

Schritte zur Lösung

y^{'''} (x) - y^{''} (x) - 25 y^{'} (x) + 25 y = 4 - e^{x} + e^{5 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 5 x} + c_{3} e^{5 x} + \frac{4}{25} + \frac{e ^{x} x}{24} + \frac{e ^{5 x} x}{40}

y = c_{1} e^{x} + c_{2} e^{- 5 x} + c_{3} e^{5 x} + \frac{4}{25} + \frac{e ^{x} x}{24} + \frac{e ^{5 x} x}{40}

y^{^{''}} + 4 y = 3, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 4 y^{^{'}} + 4 = e^{- t}

y^{^{''}} - 4 y^{^{'}} + 4 y = 3

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

2 y^{^{''}} + y^{^{'}} - 10 y = x e^{3 x} cos (π x)