(d^3+2d^2-5d-6)y=6^{-3}x

Lösung

(d^{3} + 2 d^{2} - 5 d - 6) y = 6^{- 3} x

y = c_{1} e^{- x} + c_{2} e^{2 x} + c_{3} e^{- 3 x} - \frac{x}{1296} + \frac{5}{7776}

Schritte zur Lösung

(d^{3} + 2 d^{2} - 5 d - 6) y = 6^{- 3} x

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{2 x} + c_{3} e^{- 3 x} - \frac{x}{1296} + \frac{5}{7776}

y = c_{1} e^{- x} + c_{2} e^{2 x} + c_{3} e^{- 3 x} - \frac{x}{1296} + \frac{5}{7776}

y^{^{''}} + 8 y^{^{'}} + 15 y = 10, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} - 36 y = 6 e^{2} x

- x^{^{''}} + x = 4

y^{^{''}} - y^{^{'}} - 2 y - 3 = - 6 x

d (a sin (t)) = d x