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Beliebt Rechnen >

y^{''}+5y^'+14y=0

Lösung

y^{^{''}} + 5 y^{^{'}} + 14 y = 0

Lösung

y = e^{- \frac{5 t}{2}} (c_{1} cos (\frac{31 t}{2}) + c_{2} sin (\frac{31 t}{2}))

Schritte zur Lösung

y^{''} (t) + 5 y^{'} (t) + 14 y = 0

Solve linear ODE:

y = e^{- \frac{5 t}{2}} (c_{1} cos (\frac{31 t}{2}) + c_{2} sin (\frac{31 t}{2}))

y = e^{- \frac{5 t}{2}} (c_{1} cos (\frac{31 t}{2}) + c_{2} sin (\frac{31 t}{2}))

Graph

Beliebte Beispiele

2x^{''}+8x^'+52x=0

2 x^{^{''}} + 8 x^{^{'}} + 52 x = 0

y^{'''}+4y^{''}-7y^'-10y=0

y^{^{'''}} + 4 y^{^{''}} - 7 y^{^{'}} - 10 y = 0

y^{''}+8y^'+16y=0,y(0)=5,y^'(0)=0

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (0) = 5, y^{^{'}} (0) = 0

(y^{''''}+8y^{''}+16y)^2=0

(y^{^{''''}} + 8 y^{^{''}} + 16 y)^{2} = 0

y^{''}+5y^'+4y=0,y(0)=0,y^'(0)=1

y^{^{''}} + 5 y^{^{'}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = 1