y^{'''}-2y^{''}-4y^'+8y=6xe^{2x}

Lösung

y^{^{'''}} - 2 y^{^{''}} - 4 y^{^{'}} + 8 y = 6 x e^{2 x}

y = c_{1} e^{- 2 x} + c_{2} e^{2 x} + c_{3} x e^{2 x} + \frac{32 e ^{2 x} x ^{3} - 24 e ^{2 x} x ^{2} + 12 e ^{2 x} x - 3 e ^{2 x}}{128}

Schritte zur Lösung

y^{'''} (x) - 2 y^{''} (x) - 4 y^{'} (x) + 8 y = 6 x e^{2 x}

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{2 x} + c_{3} x e^{2 x} + \frac{32 e ^{2 x} x ^{3} - 24 e ^{2 x} x ^{2} + 12 e ^{2 x} x - 3 e ^{2 x}}{128}

y = c_{1} e^{- 2 x} + c_{2} e^{2 x} + c_{3} x e^{2 x} + \frac{32 e ^{2 x} x ^{3} - 24 e ^{2 x} x ^{2} + 12 e ^{2 x} x - 3 e ^{2 x}}{128}

\int \frac{13}{( x - 7 ) ( x + 6 )} d x

f (x) = tan (x^{2})

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

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{- x}, y (0) = 4, y^{^{'}} (0) = - 1

\frac{d}{d x} (x (x^{2} - 5)^{\frac{1}{3}})