y^{''}-9y=(9t)/(e^{3t)}

Lösung

y^{^{''}} - 9 y = \frac{9 t}{e ^{3 t}}

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} + \frac{- e ^{- 3 t} t - 3 e ^{- 3 t} t ^{2}}{4} - \frac{e ^{- 3 t}}{24}

Schritte zur Lösung

y^{''} (t) - 9 y = \frac{9 t}{e ^{3 t}}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} + \frac{- e ^{- 3 t} t - 3 e ^{- 3 t} t ^{2}}{4} - \frac{e ^{- 3 t}}{24}

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} + \frac{- e ^{- 3 t} t - 3 e ^{- 3 t} t ^{2}}{4} - \frac{e ^{- 3 t}}{24}

\frac{d ^{2} x}{d t ^{2}} - 3 \frac{d x}{d t} + 12 x = 9 t

y^{^{''}} + y^{^{'}} + 5 y = 2 x

y^{^{''}} - 4 y^{^{'}} + 13 y = e^{2 t} \cdot sin (3 t), y (0) = 4

y^{^{''}} + y^{^{'}} = e^{x} + 3 x

l in e a r y^{^{''}} + 4 y = x^{2} + 5 cos (x)