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Beliebt Rechnen >

(d^2y)/(dt^2)+6(dy)/(dt)+9y=0,y(0)=2

Lösung

\frac{d ^{2} y}{d t ^{2}} + 6 \frac{d y}{d t} + 9 y = 0, y (0) = 2

Lösung

y = 2 e^{- 3 t} + c_{2} t e^{- 3 t}

Schritte zur Lösung

\frac{d ^{2} y}{d t ^{2}} + 6 \frac{d y}{d t} + 9 y = 0

Solve linear ODE:

y = 2 e^{- 3 t} + c_{2} t e^{- 3 t}

y = 2 e^{- 3 t} + c_{2} t e^{- 3 t}

Graph

Beliebte Beispiele

x^{''}+3x^'-4x=0

x^{^{''}} + 3 x^{^{'}} - 4 x = 0

y^{''}+16y^'+73y=0,y(0)=4

y^{^{''}} + 16 y^{^{'}} + 73 y = 0, y (0) = 4

y^{''}+6y^'+10y=0,y(pi/2)=0,y^'(pi/2)=9

y^{^{''}} + 6 y^{^{'}} + 10 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 9

y^{''}-y^'+144y=0

y^{^{''}} - y^{^{'}} + 144 y = 0

y^{''}+64y=0,y(0)=0,y^'(0)=8

y^{^{''}} + 64 y = 0, y (0) = 0, y^{^{'}} (0) = 8