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Beliebt Rechnen >

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

Lösung

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

Lösung

y = (1 - \frac{5}{7}) e^{4 t} + \frac{5}{7} e^{- 3 t}

Schritte zur Lösung

y^{''} (t) - y^{'} (t) - 12 y = 0

Solve linear ODE:

y = (1 - \frac{5}{7}) e^{4 t} + \frac{5}{7} e^{- 3 t}

y = (1 - \frac{5}{7}) e^{4 t} + \frac{5}{7} e^{- 3 t}

Graph

Beliebte Beispiele

24y^{''}+7y^'-5y=0

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

2y^{''}+12y^'+18y=0

2 y^{^{''}} + 12 y^{^{'}} + 18 y = 0

y^{''}+2y^'+9y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 2 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = 0

3x^{''}-7x^'+4x=0

3 x^{^{''}} - 7 x^{^{'}} + 4 x = 0

y^{''}+4y^'-5y=0,y(ln(2))=3,y(0)=33

y^{^{''}} + 4 y^{^{'}} - 5 y = 0, y (ln (2)) = 3, y (0) = 33