y^{'''}-y^{''}-25y^'+25y=7-e^x+e^{5x}

Lösung

y^{^{'''}} - y^{^{''}} - 25 y^{^{'}} + 25 y = 7 - e^{x} + e^{5 x}

y = c_{1} e^{x} + c_{2} e^{- 5 x} + c_{3} e^{5 x} + \frac{7}{25} + \frac{e ^{x} x}{24} + \frac{e ^{5 x} x}{40}

Schritte zur Lösung

y^{'''} (x) - y^{''} (x) - 25 y^{'} (x) + 25 y = 7 - e^{x} + e^{5 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 5 x} + c_{3} e^{5 x} + \frac{7}{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{7}{25} + \frac{e ^{x} x}{24} + \frac{e ^{5 x} x}{40}

(D^{2} + D - 2) y = e^{x}

y^{^{''}} - 8 y^{^{'}} + 15 y = e^{3 x} sin (3 x)

x^{^{''}} + a^{2} x = a^{2} b + c

y^{^{''}} - 10 y^{^{'}} + 9 y = 5

y^{^{''}} - 8 y^{^{'}} + 20 y = 200 x^{2} - 78 x e^{x}