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Beliebt Rechnen >

y^{''}+6y^'+9y=12e^t

Lösung

y^{^{''}} + 6 y^{^{'}} + 9 y = 12 e^{t}

Lösung

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

Schritte zur Lösung

y^{''} (t) + 6 y^{'} (t) + 9 y = 12 e^{t}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

2y^{''}+8y^'+80y=1,y(0)=0,y^'(0)=0

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 1, y (0) = 0, y^{^{'}} (0) = 0

D(x)=sqrt(82.5-2*5x)

D (x) = 82.5 - 2 \cdot 5 x

y^{^{''}} + 6 y = 8 t

y^{''}-y^'-6y=12cos(3x)

y^{^{''}} - y^{^{'}} - 6 y = 12 cos (3 x)

x^{''}+5x^'+6x=10

x^{^{''}} + 5 x^{^{'}} + 6 x = 10