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Beliebt Rechnen >

y^{''}+ky^'+8y=0

Lösung

y^{^{''}} + k y^{^{'}} + 8 y = 0

Lösung

y = c_{1} e^{\frac{t ( - k + k ^{2} - 32 )}{2}} + c_{2} e^{\frac{t ( - k - k ^{2} - 32 )}{2}}

Schritte zur Lösung

y^{''} (t) + k y^{'} (t) + 8 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{t ( - k + k ^{2} - 32 )}{2}} + c_{2} e^{\frac{t ( - k - k ^{2} - 32 )}{2}}

y = c_{1} e^{\frac{t ( - k + k ^{2} - 32 )}{2}} + c_{2} e^{\frac{t ( - k - k ^{2} - 32 )}{2}}

Graph

Beliebte Beispiele

100y^{''}-140y^'+85y=0,y(2)=9,y^'(2)=8

100 y^{^{''}} - 140 y^{^{'}} + 85 y = 0, y (2) = 9, y^{^{'}} (2) = 8

x^{^{''}} - 6 x = 0

y^{''}+y^'-10/3 y=0

y^{^{''}} + y^{^{'}} - \frac{10}{3} y = 0

x^{''}+8x^'+4x=0

x^{^{''}} + 8 x^{^{'}} + 4 x = 0

(d^3y)/(dx^3)+(dy)/(dx)=0

\frac{d ^{3} y}{d x ^{3}} + \frac{d y}{d x} = 0