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

Lösung

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

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{x ^{3}}{5} - \frac{12 x ^{2}}{25} + \frac{66 x}{125} - \frac{144}{625}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{x ^{3}}{5} - \frac{12 x ^{2}}{25} + \frac{66 x}{125} - \frac{144}{625}

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{x ^{3}}{5} - \frac{12 x ^{2}}{25} + \frac{66 x}{125} - \frac{144}{625}

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

y^{^{''}} + 4 y^{^{'}} + 4 y = \frac{e ^{- 2} x}{x ^{3}}

x^{^{'''}} - x = 3 e^{t}

y^{^{'''}} + y^{^{'}} + 2 = 0

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