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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+9y=sin(3x)+e^{-x}

y^{^{''}} + 9 y = sin (3 x) + e^{- x}

(D^2-2D+1)y=x^2e^{3x}

(D^{2} - 2 D + 1) y = x^{2} e^{3 x}

(d^2-1)y=xsin(x)+(1+x^2)e^x

(d^{2} - 1) y = x sin (x) + (1 + x^{2}) e^{x}

3x^{''}-30x^'+75x=2t+1

3 x^{^{''}} - 30 x^{^{'}} + 75 x = 2 t + 1

y^{''}+y^'-6y=12e^{3t}+12e^{-2t}

y^{^{''}} + y^{^{'}} - 6 y = 12 e^{3 t} + 12 e^{- 2 t}