y^{'''}-y^{''}-16y^'+16y=3-e^x+e^{4x}

Lösung

y^{^{'''}} - y^{^{''}} - 16 y^{^{'}} + 16 y = 3 - e^{x} + e^{4 x}

y = c_{1} e^{x} + c_{2} e^{- 4 x} + c_{3} e^{4 x} + \frac{3}{16} + \frac{e ^{x} x}{15} + \frac{e ^{4 x} x}{24}

Schritte zur Lösung

y^{'''} (x) - y^{''} (x) - 16 y^{'} (x) + 16 y = 3 - e^{x} + e^{4 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 4 x} + c_{3} e^{4 x} + \frac{3}{16} + \frac{e ^{x} x}{15} + \frac{e ^{4 x} x}{24}

y = c_{1} e^{x} + c_{2} e^{- 4 x} + c_{3} e^{4 x} + \frac{3}{16} + \frac{e ^{x} x}{15} + \frac{e ^{4 x} x}{24}

l in e a r y^{^{''}} - 6 y^{^{'}} + 9 y = 3 x^{2} + 4 e^{4 x}

y^{^{''}} + 4 y^{^{'}} + 3 y = 8 x e^{x} - 6

y^{^{''}} + 3 y^{^{'}} - 10 y = e^{- 5 x}

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

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