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Beliebt Rechnen >

4y+9y^{''}=-12y^'

Lösung

4 y + 9 y^{^{''}} = - 12 y^{^{'}}

Lösung

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

Schritte zur Lösung

4 y + 9 y^{''} (t) = - 12 y^{'} (t)

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

9y^{''}+12y^'+4y=0,y(0)=1,y^'(0)=0

9 y^{^{''}} + 12 y^{^{'}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{''}-7y^'+12y=0,y(0)=3,y^'(0)=0

y^{^{''}} - 7 y^{^{'}} + 12 y = 0, y (0) = 3, y^{^{'}} (0) = 0

x^{''}+5x^'-6x=0

x^{^{''}} + 5 x^{^{'}} - 6 x = 0

2y^{''}+6y^'+8y=0

2 y^{^{''}} + 6 y^{^{'}} + 8 y = 0

y^{'''}-y^{''}+2y^'-2y=0

y^{^{'''}} - y^{^{''}} + 2 y^{^{'}} - 2 y = 0