y^{'''}-y^{''}-9y^'+9y=7-e^x+e^{3x}

Lösung

y^{^{'''}} - y^{^{''}} - 9 y^{^{'}} + 9 y = 7 - e^{x} + e^{3 x}

y = c_{1} e^{x} + c_{2} e^{- 3 x} + c_{3} e^{3 x} + \frac{7}{9} + \frac{e ^{x} x}{8} + \frac{e ^{3 x} x}{12}

Schritte zur Lösung

y^{'''} (x) - y^{''} (x) - 9 y^{'} (x) + 9 y = 7 - e^{x} + e^{3 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 3 x} + c_{3} e^{3 x} + \frac{7}{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{7}{9} + \frac{e ^{x} x}{8} + \frac{e ^{3 x} x}{12}

3 y^{^{''}} - y = e^{x} - 5

y^{^{''}} + 4 y^{^{'}} + 4 y = 375 \cdot t

y^{^{''}} - 2 y^{^{'}} - 15 y = 4 e^{t}

y^{^{'''}} + 3 y^{^{''}} + 2 y^{^{'}} = u

y^{^{''}} - 2 y^{^{'}} + 2 y = 2 x^{2} - 2 x + 1 + sin (x)