y^{'''}-y^{''}-9y^'+9y=4-e^x+e^{3x}

Lösung

y^{^{'''}} - y^{^{''}} - 9 y^{^{'}} + 9 y = 4 - e^{x} + e^{3 x}

y = c_{1} e^{x} + c_{2} e^{- 3 x} + c_{3} e^{3 x} + \frac{4}{9} + \frac{e ^{x} x}{8} + \frac{e ^{3 x} x}{12}

Schritte zur Lösung

y^{'''} (x) - y^{''} (x) - 9 y^{'} (x) + 9 y = 4 - e^{x} + e^{3 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 3 x} + c_{3} e^{3 x} + \frac{4}{9} + \frac{e ^{x} x}{8} + \frac{e ^{3 x} x}{12}

y = c_{1} e^{x} + c_{2} e^{- 3 x} + c_{3} e^{3 x} + \frac{4}{9} + \frac{e ^{x} x}{8} + \frac{e ^{3 x} x}{12}

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

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

y^{^{''}} - 2 y^{^{'}} + y = 12 x^{3} e^{x}

2 y^{^{''}} - 2 y^{^{'}} - 4 y = 2 e^{2 t}

y^{^{'''}} + 6 y^{^{''}} + 11 y^{^{'}} + 6 y = 3 + 3 x