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Beliebt Rechnen >

4x^{''}+12x^'+9x=0

Lösung

4 x^{^{''}} + 12 x^{^{'}} + 9 x = 0

Lösung

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

Schritte zur Lösung

4 x^{''} (t) + 12 x^{'} (t) + 9 x = 0

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{'''}+10y^{''}+9y^'=0

y^{^{'''}} + 10 y^{^{''}} + 9 y^{^{'}} = 0

y^{''}-3y^'+2y=0,y(0)=0,y^'(0)=1

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{''}-7y^'+10y=0,y^'(0)=-1/3

y^{^{''}} - 7 y^{^{'}} + 10 y = 0, y^{^{'}} (0) = - \frac{1}{3}

(D^{2} - 6 D + 25) y = 0

4y^{''}+4y^'+y=0,y(0)=-1,y^'(0)=2

4 y^{^{''}} + 4 y^{^{'}} + y = 0, y (0) = - 1, y^{^{'}} (0) = 2