y^{''}+4y^'+5y=15x+e^{-x}

Lösung

y^{^{''}} + 4 y^{^{'}} + 5 y = 15 x + e^{- x}

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + 3 x - \frac{12}{5} + \frac{1}{2} e^{- x}

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 5 y = 15 x + e^{- x}

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + 3 x - \frac{12}{5} + \frac{1}{2} e^{- x}

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + 3 x - \frac{12}{5} + \frac{1}{2} e^{- x}

\frac{d}{d x} (\frac{sin ( x )}{1 + sin ( x )})

\int_{1}^{\infty} (\frac{1}{x ^{3}}) d x

l a pl a ce t r an s f or m 4 t^{2} cos (2 t) + 5 t e^{- 7 t}

\frac{d}{d x} (4 x^{9} + 2 x^{5})

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