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Beliebt Rechnen >

2x^{''}+2x^'+3x=0

Lösung

2 x^{^{''}} + 2 x^{^{'}} + 3 x = 0

Lösung

x = e^{- \frac{t}{2}} (c_{1} cos (\frac{5 t}{2}) + c_{2} sin (\frac{5 t}{2}))

Schritte zur Lösung

2 x^{''} (t) + 2 x^{'} (t) + 3 x = 0

Solve linear ODE:

x = e^{- \frac{t}{2}} (c_{1} cos (\frac{5 t}{2}) + c_{2} sin (\frac{5 t}{2}))

x = e^{- \frac{t}{2}} (c_{1} cos (\frac{5 t}{2}) + c_{2} sin (\frac{5 t}{2}))

Graph

Beliebte Beispiele

3y^{''}+2y^'+4y^{''}+y=0

3 y^{^{''}} + 2 y^{^{'}} + 4 y^{^{''}} + y = 0

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

4y^{''}-y^'-3y=0,y(0)=5,y^'(0)=0

4 y^{^{''}} - y^{^{'}} - 3 y = 0, y (0) = 5, y^{^{'}} (0) = 0

y^{''''}-7y^{'''}+12y^{''}=0

y^{^{''''}} - 7 y^{^{'''}} + 12 y^{^{''}} = 0

y^{''}+6y^{''}+11y^'+6y=0

y^{^{''}} + 6 y^{^{''}} + 11 y^{^{'}} + 6 y = 0