y^{'''}-6y^{''}+12y^'-8y=6e^{2x}+16x^2

Lösung

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = 6 e^{2 x} + 16 x^{2}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + c_{3} x^{2} e^{2 x} + e^{2 x} x^{3} - 2 x^{2} - 6 x - 6

Schritte zur Lösung

y^{'''} (x) - 6 y^{''} (x) + 12 y^{'} (x) - 8 y = 6 e^{2 x} + 16 x^{2}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + c_{3} x^{2} e^{2 x} + e^{2 x} x^{3} - 2 x^{2} - 6 x - 6

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + c_{3} x^{2} e^{2 x} + e^{2 x} x^{3} - 2 x^{2} - 6 x - 6

y^{^{''}} + 4 y = \frac{3}{sin ( 2 x )}

a y^{^{''}} + 2 y^{^{'}} = 4 e^{2 t}, y (0) = 0, y^{^{'}} (0) = 0

(D^{2} + 3 D) y = - 18 x

y^{^{''}} - 2 y^{^{'}} - 8 y = 4 e^{2} - 21 e^{- 3 x}

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