y^{''}-8y^'+25y=5x^3e^{-x}-7e^{-x}

Lösung

y^{^{''}} - 8 y^{^{'}} + 25 y = 5 x^{3} e^{- x} - 7 e^{- x}

y = e^{4 x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{5 e ^{- x} x ^{3}}{34} + \frac{75 e ^{- x} x ^{2}}{578} + \frac{495 e ^{- x} x}{9826} - \frac{33191}{167042} e^{- x}

Schritte zur Lösung

y^{''} (x) - 8 y^{'} (x) + 25 y = 5 x^{3} e^{- x} - 7 e^{- x}

Solve linear ODE:

y = e^{4 x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{5 e ^{- x} x ^{3}}{34} + \frac{75 e ^{- x} x ^{2}}{578} + \frac{495 e ^{- x} x}{9826} - \frac{33191}{167042} e^{- x}

y = e^{4 x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{5 e ^{- x} x ^{3}}{34} + \frac{75 e ^{- x} x ^{2}}{578} + \frac{495 e ^{- x} x}{9826} - \frac{33191}{167042} e^{- x}

\frac{d}{d x} (\frac{3 x ^{5} + 7}{x ^{3}})

d er i v a t i v e f (x) = e^{x^{6}} - x + 1

\int (6 t^{2} \cdot 3 t) d t

\frac{\partial}{\partial y} (x - y^{2})

a re a y = - x^{2} + 4, y = 3 x