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Beliebt Rechnen >

y^{''}+4y^'+68y=0,y(0)=7

Lösung

y^{^{''}} + 4 y^{^{'}} + 68 y = 0, y (0) = 7

Lösung

y = e^{- 2 t} (7 cos (8 t) + c_{2} sin (8 t))

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) + 68 y = 0

Solve linear ODE:

y = e^{- 2 t} (7 cos (8 t) + c_{2} sin (8 t))

y = e^{- 2 t} (7 cos (8 t) + c_{2} sin (8 t))

Graph

Beliebte Beispiele

2x^{''}+32x=0,x(0)=0,x^'(0)=0

2 x^{^{''}} + 32 x = 0, x (0) = 0, x^{^{'}} (0) = 0

y^{'''}+2y^{''}-11y^'-52y=0

y^{^{'''}} + 2 y^{^{''}} - 11 y^{^{'}} - 52 y = 0

(d^2f)/(dx^2)+64f(x)=0

\frac{d ^{2} f}{d x ^{2}} + 64 f (x) = 0

5y^{''}-7y^'+2y=0,y(0)=1,y^'(0)=-0.8y

5 y^{^{''}} - 7 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = - 0.8 y

(D^3-D^2-8D+12)y=0

(D^{3} - D^{2} - 8 D + 12) y = 0