y^{''}+4y^'+5y=-10x+3e^{-x}

Lösung

y^{^{''}} + 4 y^{^{'}} + 5 y = - 10 x + 3 e^{- x}

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) - 2 x + \frac{8}{5} + \frac{3}{2} e^{- x}

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 5 y = - 10 x + 3 e^{- x}

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) - 2 x + \frac{8}{5} + \frac{3}{2} e^{- x}

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) - 2 x + \frac{8}{5} + \frac{3}{2} e^{- x}

x \to 3 lim (x - 2)

\int \frac{sec ^{2} ( x )}{x} d x

d er i v a t i v e f (x) = \frac{x + 5}{x - 5}

x \to - 2 lim (x^{2} - \frac{4}{x + 2})

a re a y = cos (x), y = 0.5, 0 \leq x \leq π