y^{'''}-2y^{''}-y^'+2y=e^4x

Lösung

y^{^{'''}} - 2 y^{^{''}} - y^{^{'}} + 2 y = e^{4} x

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

Schritte zur Lösung

y^{'''} (x) - 2 y^{''} (x) - y^{'} (x) + 2 y = e^{4} x

Solve linear ODE:

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

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

y^{^{''}} + 9 y^{^{'}} = sin (t), y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} + 9 y = 5 sin (3 x), y (0) = 6, y^{^{'}} (0) = 0

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

y^{^{''}} - 6 y^{^{'}} + 13 y = 4.29 e^{3 t} \cdot cos (4.29 t)

5 y^{^{''}} - 10 y^{^{'}} + 10 y = e^{x} \cdot sec (x)