(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}

(d^{4} - 1) y = e^{x} cos (x) cos^{3} (x)

(d^{2} - 4 d + 4) \cdot y = 8 e^{2 x} \cdot x^{2} \cdot sin^{2} (x)

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 t - 8

(d^{3} - 2 d + 4) y = 3 x^{2} - 5 x + 2

(d^{3} - 3 d^{2} + 4 d - 2) \cdot y = e^{x} + cos (x) + x