y^{'''}-y^{''}-25y^'+25y=2-e^x+e^{5x}

Lösung

y^{^{'''}} - y^{^{''}} - 25 y^{^{'}} + 25 y = 2 - e^{x} + e^{5 x}

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

Schritte zur Lösung

y^{'''} (x) - y^{''} (x) - 25 y^{'} (x) + 25 y = 2 - e^{x} + e^{5 x}

Solve linear ODE:

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

y^{^{''}} - 4 y^{^{'}} = 2 cos^{2} (4 x)

y^{^{''}} + 2 y^{^{'}} - 3 y = 16 e^{- 3 t}

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{- t}

(D^{2} - 3 D + 2) y = 2 x^{3} - 9 x^{2} + 6 x

y^{^{''}} + 6 y^{^{'}} + 13 y = 7 cos (3 t + \frac{π}{4})