y^{''}+4y^'+4y=e^{-2x}

Lösung

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{- 2 x}

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{e ^{- 2 x} x ^{2}}{2}

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 4 y = e^{- 2 x}

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{e ^{- 2 x} x ^{2}}{2}

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{e ^{- 2 x} x ^{2}}{2}

a re a x = 6 y^{2}, x = 4 + 2 y^{2}

t an g e n t f (x) = x (x^{6} - 1), at x = 1

\int e^{x} \cdot cos (3 x) d x

\int \frac{6 x ^{2} - 15 x + 22}{( x + 3 ) ( x ^{2} + 2 ) ^{2}} d x

t an g e n t y = \frac{1}{x}, (4, \frac{1}{2})