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Beliebt Rechnen >

y^{''}-4y^'-5y=0,y(0)=1,y^'(0)=2

Lösung

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (0) = 1, y^{^{'}} (0) = 2

Lösung

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

Schritte zur Lösung

y^{''} (t) - 4 y^{'} (t) - 5 y = 0

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{'''}+5y^{''}-13y^'+7y=0

y^{^{'''}} + 5 y^{^{''}} - 13 y^{^{'}} + 7 y = 0

0.05y^{''}+2y^'+100y=0,y(0)=5,y^'(0)=0

0.05 y^{^{''}} + 2 y^{^{'}} + 100 y = 0, y (0) = 5, y^{^{'}} (0) = 0

(D^{4} - 81) y = 0

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

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

y^{''}-12y^'+ay=0,y(0)=1,y^'(0)=16

y^{^{''}} - 12 y^{^{'}} + a y = 0, y (0) = 1, y^{^{'}} (0) = 16