(D^2+5D+4)Y=x^2+7x+9

Lösung

(D^{2} + 5 D + 4) Y = x^{2} + 7 x + 9

Y (x) = c_{1} e^{- x} + c_{2} e^{- 4 x} + \frac{x ^{2}}{4} + \frac{9 x}{8} + \frac{23}{32}

Schritte zur Lösung

(D^{2} + 5 D + 4) Y (x) = x^{2} + 7 x + 9

Solve linear ODE:

Y (x) = c_{1} e^{- x} + c_{2} e^{- 4 x} + \frac{x ^{2}}{4} + \frac{9 x}{8} + \frac{23}{32}

Y (x) = c_{1} e^{- x} + c_{2} e^{- 4 x} + \frac{x ^{2}}{4} + \frac{9 x}{8} + \frac{23}{32}

y^{^{''}} + 2 y^{^{'}} - 15 y = 7 e^{3 t} + (1 - 2 t) sin (6 t)

y^{^{''}} + 2 y^{^{'}} + 2 y = g (t), y (0) = 8, y^{^{'}} (0) = 6

y^{^{''}} - 4 y = 1, y^{^{'}} (0) = 2

y^{^{''}} - 16 y = 19.2 e^{4 x} + 60 e^{x}

y^{^{''}} - 2 y^{^{'}} + 5 y = 2 (cos^{2} (x)) e^{x}