y^{''}+4y^'+4y=-(18te-2t+8t+4)

Lösung

y^{^{''}} + 4 y^{^{'}} + 4 y = - (18 t e - 2 t + 8 t + 4)

y = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} + \frac{( - 18 e - 6 ) t}{4} + \frac{18 e + 2}{4}

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) + 4 y = - (18 t e - 2 t + 8 t + 4)

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} + \frac{( - 18 e - 6 ) t}{4} + \frac{18 e + 2}{4}

y = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} + \frac{( - 18 e - 6 ) t}{4} + \frac{18 e + 2}{4}

\frac{\partial}{\partial x} (5 x^{7} cos (y^{8}))

x \to 0 lim (1 + sin (x) - e^{x})

\int - x^{2} + x + 2 d x

\frac{d y}{d x} = k y^{2} ln (x)

x \to 0 lim (1 - \frac{2}{3 x})