(d^3-7d-6)y=e^2x(1+x)

Lösung

(d^{3} - 7 d - 6) y = e^{2} x (1 + x)

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} - \frac{e ^{2} x ^{2}}{6} + \frac{2 e ^{2} x}{9} - \frac{7 e ^{2}}{27}

Schritte zur Lösung

(d^{3} - 7 d - 6) y = e^{2} x (1 + x)

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} - \frac{e ^{2} x ^{2}}{6} + \frac{2 e ^{2} x}{9} - \frac{7 e ^{2}}{27}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} - \frac{e ^{2} x ^{2}}{6} + \frac{2 e ^{2} x}{9} - \frac{7 e ^{2}}{27}

(d^{4} - 1) y = 7 x^{2}

(d^{3} - 5 d^{2} + 8 d - 4) y = e^{2} x

(d + 2 d^{2} + 1) y = cos (x)

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

y^{^{'''}} - 3 y^{^{'}} + 2 y = 9 e^{x}