y^{'''}+y^{''}-2y=e^{3x}(9+67x+17x^2)

Lösung

y^{^{'''}} + y^{^{''}} - 2 y = e^{3 x} (9 + 67 x + 17 x^{2})

y = c_{1} e^{x} + e^{- x} (c_{2} cos (x) + c_{3} sin (x)) + \frac{e ^{3 x} x ^{2}}{2} + e^{3 x} x - e^{3 x}

Schritte zur Lösung

y^{'''} (x) + y^{''} (x) - 2 y = e^{3 x} (9 + 67 x + 17 x^{2})

Solve linear ODE:

y = c_{1} e^{x} + e^{- x} (c_{2} cos (x) + c_{3} sin (x)) + \frac{e ^{3 x} x ^{2}}{2} + e^{3 x} x - e^{3 x}

y = c_{1} e^{x} + e^{- x} (c_{2} cos (x) + c_{3} sin (x)) + \frac{e ^{3 x} x ^{2}}{2} + e^{3 x} x - e^{3 x}

y^{^{''}} - 8 y^{^{'}} + 80 y = - 2 sin (3 t)

0.25 y^{^{''}} + 0.25 y^{^{'}} + 16 y = 3 cos (2 t)

y^{^{''}} - 4 y^{^{'}} + 40 y = t e^{2 t} sin (6 t)

y^{^{''}} + 3 y^{^{'}} - 7 y = t^{4} e^{t}

x^{^{''}} - 16 x^{^{'}} + 64 x = t e^{8 t}