y^{''}+5y^'+4y=8te^{2t}

Lösung

y^{^{''}} + 5 y^{^{'}} + 4 y = 8 t e^{2 t}

y = c_{1} e^{- t} + c_{2} e^{- 4 t} + \frac{4 e ^{2 t} t}{9} - \frac{2}{9} e^{2 t}

Schritte zur Lösung

y^{''} (t) + 5 y^{'} (t) + 4 y = 8 t e^{2 t}

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 4 t} + \frac{4 e ^{2 t} t}{9} - \frac{2}{9} e^{2 t}

y = c_{1} e^{- t} + c_{2} e^{- 4 t} + \frac{4 e ^{2 t} t}{9} - \frac{2}{9} e^{2 t}

x \to + 0 + lim (3 x)

d er i v a t i v e f (x) = x^{2} 4 x - 1

l a pl a ce t r an s f or m sin (5 t - \frac{π}{3}) \cdot 1 (5 t - \frac{π}{3})

in v erse l a pl a ce \frac{3 z - 5}{z ^{2} - 4 z + 3}

\int_{1}^{3} \frac{e ^{\frac{3}{x}}}{x ^{2}} d x