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Beliebt Rechnen >

y^{''}-8y^'+16y=t^{-3}e^{4t}

Lösung

y^{^{''}} - 8 y^{^{'}} + 16 y = t^{- 3} e^{4 t}

Lösung

y = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{e ^{4 t}}{2 t}

Schritte zur Lösung

y^{''} (t) - 8 y^{'} (t) + 16 y = t^{- 3} e^{4 t}

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{e ^{4 t}}{2 t}

y = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{e ^{4 t}}{2 t}

Graph

Beliebte Beispiele

(16+x^2)((dy)/(dx))-2xy=0

(16 + x^{2}) (\frac{d y}{d x}) - 2 x y = 0

derivative ln((x^2)/(3-x))

d er i v a t i v e ln (\frac{x ^{2}}{3 - x})

(dy)/(dx)=3y^{2/3}

\frac{d y}{d x} = 3 y^{\frac{2}{3}}

(\partial)/(\partial y)(2xy^4+2)

\frac{\partial}{\partial y} (2 x y^{4} + 2)

limit as x approaches 0 of 1/(2x)

x \to 0 lim (\frac{1}{2 x})