(D^2-4D+4)y=e^x+x^2+cos(2x)

Lösung

(D^{2} - 4 D + 4) y = e^{x} + x^{2} + cos (2 x)

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + e^{x} + \frac{x ^{2}}{4} + \frac{x}{2} + \frac{3}{8} - \frac{1}{8} sin (2 x)

Schritte zur Lösung

(D^{2} - 4 D + 4) y = e^{x} + x^{2} + cos (2 x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + e^{x} + \frac{x ^{2}}{4} + \frac{x}{2} + \frac{3}{8} - \frac{1}{8} sin (2 x)

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + e^{x} + \frac{x ^{2}}{4} + \frac{x}{2} + \frac{3}{8} - \frac{1}{8} sin (2 x)

y^{^{''}} + 8 y^{^{'}} + 17 y = 2 e^{- 4 t} cos (t)

y^{^{''}} - 8 y^{^{'}} + 20 y = 100 x^{2} + 26 x e^{x}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} 4 + 8 y = 8 x^{2}

y^{^{''}} - 2 y^{^{'}} = x^{2} - 1

\frac{1}{4} y^{^{''}} + y^{^{'}} + y = sin (x)