y^{''}-y^'-6y=2e^{2t}-t^2-2t+3

Lösung

y^{^{''}} - y^{^{'}} - 6 y = 2 e^{2 t} - t^{2} - 2 t + 3

y = c_{1} e^{3 t} + c_{2} e^{- 2 t} - \frac{1}{2} e^{2 t} + \frac{t ^{2}}{6} + \frac{5 t}{18} - \frac{53}{108}

Schritte zur Lösung

y^{''} (t) - y^{'} (t) - 6 y = 2 e^{2 t} - t^{2} - 2 t + 3

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 2 t} - \frac{1}{2} e^{2 t} + \frac{t ^{2}}{6} + \frac{5 t}{18} - \frac{53}{108}

y = c_{1} e^{3 t} + c_{2} e^{- 2 t} - \frac{1}{2} e^{2 t} + \frac{t ^{2}}{6} + \frac{5 t}{18} - \frac{53}{108}

x \to 6 lim (\frac{x ^{2} + 2 x - 48}{3 x ^{2} - 20 x + 12})

s im pl i f y \frac{- ln ( 1 + 6 x )}{x}

\frac{d}{d x} (ln (x^{2} + x + 1))

im pl i c i t 3 x^{3} + 2 y^{3} = 12

\frac{d y}{d x} = \frac{x + 6}{x + 1}