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Beliebt Rechnen >

y^{''}+6y^'+16y=0,y(0)=4,y^'(0)=0

Lösung

y^{^{''}} + 6 y^{^{'}} + 16 y = 0, y (0) = 4, y^{^{'}} (0) = 0

Lösung

y = e^{- 3 t} (4 cos (7 t) + \frac{12}{7} sin (7 t))

Schritte zur Lösung

y^{''} (t) + 6 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = e^{- 3 t} (4 cos (7 t) + \frac{12}{7} sin (7 t))

y = e^{- 3 t} (4 cos (7 t) + \frac{12}{7} sin (7 t))

Graph

Beliebte Beispiele

5y^{''}-30y^'+170y=0

5 y^{^{''}} - 30 y^{^{'}} + 170 y = 0

y^{''}+14y^'+49y=0,y(-4)=1,y^'(-4)=5

y^{^{''}} + 14 y^{^{'}} + 49 y = 0, y (- 4) = 1, y^{^{'}} (- 4) = 5

y^{'''}-49y^'=0

y^{^{'''}} - 49 y^{^{'}} = 0

y^{''}+2y^'+10y=0,y(0)=e^{-pi/6}

y^{^{''}} + 2 y^{^{'}} + 10 y = 0, y (0) = e^{- \frac{π}{6}}

(d^3y)/(dt^3)-(d^2y)/(dt^2)=0

\frac{d ^{3} y}{d t ^{3}} - \frac{d ^{2} y}{d t ^{2}} = 0