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

Lösung

(d + 2) \cdot (d - 1)^{3} \cdot 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^{^{'''}} - 2 y^{^{''}} + y^{^{'}} = 2 - 24 e^{x} + 40 e^{5} x

(d^{2} + 9) y = 2 x^{2}

(d^{5} - d) \cdot j = 8 sin (x) - 2 \cdot x

(d^{2} + 4) y = sin^{2} (2 x)

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