y^{'''}-y^{''}-25y^'+25y=6-e^x+e^{5x}

Lösung

y^{^{'''}} - y^{^{''}} - 25 y^{^{'}} + 25 y = 6 - e^{x} + e^{5 x}

y = c_{1} e^{x} + c_{2} e^{- 5 x} + c_{3} e^{5 x} + \frac{6}{25} + \frac{e ^{x} x}{24} + \frac{e ^{5 x} x}{40}

Schritte zur Lösung

y^{'''} (x) - y^{''} (x) - 25 y^{'} (x) + 25 y = 6 - e^{x} + e^{5 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 5 x} + c_{3} e^{5 x} + \frac{6}{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{6}{25} + \frac{e ^{x} x}{24} + \frac{e ^{5 x} x}{40}

y^{^{''''}} + 2 y^{^{''}} + y = 7 + cos (3 t)

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

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

y^{^{''}} - 5 y^{^{'}} + 6 e^{x} = 0

3 \frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + y = x - 7