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Beliebt Rechnen >

y^{''}-2y^'-8y=18te^{4t}

Lösung

y^{^{''}} - 2 y^{^{'}} - 8 y = 18 t e^{4 t}

Lösung

y = c_{1} e^{4 t} + c_{2} e^{- 2 t} + \frac{3 e ^{4 t} t ^{2}}{2} - \frac{e ^{4 t} t}{2}

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) - 8 y = 18 t e^{4 t}

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} e^{- 2 t} + \frac{3 e ^{4 t} t ^{2}}{2} - \frac{e ^{4 t} t}{2}

y = c_{1} e^{4 t} + c_{2} e^{- 2 t} + \frac{3 e ^{4 t} t ^{2}}{2} - \frac{e ^{4 t} t}{2}

Graph

Beliebte Beispiele

y^{^{''}} - 4 y = 8 x^{2}

x^{''}-4x^'+3x=(e^t)/(1+e^t)

x^{^{''}} - 4 x^{^{'}} + 3 x = \frac{e ^{t}}{1 + e ^{t}}

y^{''}-9y^'+18y=9+18x

y^{^{''}} - 9 y^{^{'}} + 18 y = 9 + 18 x

y^{''}+2y^'-3y=8e^{-3x}

y^{^{''}} + 2 y^{^{'}} - 3 y = 8 e^{- 3 x}

y^{''}+6y^'+9y=3

y^{^{''}} + 6 y^{^{'}} + 9 y = 3