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Beliebt Rechnen >

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

Lösung

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

Lösung

y = (4 - \frac{5}{2}) e^{4 t} + \frac{5}{2} e^{- 4 t}

Schritte zur Lösung

y^{''} (t) - 16 y = 0

Solve linear ODE:

y = (4 - \frac{5}{2}) e^{4 t} + \frac{5}{2} e^{- 4 t}

y = (4 - \frac{5}{2}) e^{4 t} + \frac{5}{2} e^{- 4 t}

Graph

Beliebte Beispiele

y^{''}+22y^'+αy=0,y(0)=1,y^'(0)=-25

y^{^{''}} + 22 y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = - 25

y^{''}+2/3 y^'+1/9 y=0

y^{^{''}} + \frac{2}{3} y^{^{'}} + \frac{1}{9} y = 0

(D^{2} - 2 D + 5) y = 0

y^{''}+10y^'+16y=0

y^{^{''}} + 10 y^{^{'}} + 16 y = 0

(4D^5-23D^3-33D^2-17D-3)y=0

(4 D^{5} - 23 D^{3} - 33 D^{2} - 17 D - 3) y = 0