(D+2)(D-1)^3y=e^x

Lösung

(D + 2) (D - 1)^{3} y = e^{x}

y = c_{1} e^{- 2 x} + c_{2} e^{x} + c_{3} x e^{x} + c_{4} x^{2} e^{x} + \frac{9 e ^{x} x ^{3} - 9 e ^{x} x ^{2} + 6 e ^{x} x - 2 e ^{x}}{162}

Schritte zur Lösung

(D + 2) (D - 1)^{3} y = e^{x}

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{x} + c_{3} x e^{x} + c_{4} x^{2} e^{x} + \frac{9 e ^{x} x ^{3} - 9 e ^{x} x ^{2} + 6 e ^{x} x - 2 e ^{x}}{162}

y = c_{1} e^{- 2 x} + c_{2} e^{x} + c_{3} x e^{x} + c_{4} x^{2} e^{x} + \frac{9 e ^{x} x ^{3} - 9 e ^{x} x ^{2} + 6 e ^{x} x - 2 e ^{x}}{162}

y^{^{''}} + 16 y = 5 sin (4 x)

y^{^{''}} + 9 y = cos (x), y (\frac{π}{2}) = - \frac{5}{3}, y^{^{'}} (0) = 5

(D^{2} - 3 D + 2) y = x + 1

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

y^{^{''}} + 4 y + 4 = 0