y^{''}+6y^'+9y=e^{3x}+2

Lösung

y^{^{''}} + 6 y^{^{'}} + 9 y = e^{3 x} + 2

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + \frac{1}{36} e^{3 x} + \frac{2}{9}

Schritte zur Lösung

y^{''} (x) + 6 y^{'} (x) + 9 y = e^{3 x} + 2

Solve linear ODE:

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + \frac{1}{36} e^{3 x} + \frac{2}{9}

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + \frac{1}{36} e^{3 x} + \frac{2}{9}

y^{^{''}} + 4 y = t sin^{2} (t)

y^{^{''}} - 2 y^{^{'}} - 15 = 0

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

y^{^{''}} + y = 8 sin (x) + 4 cos (x) + 1

x^{^{''}} + 4 x^{^{'}} + 4 = 0