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Beliebt Rechnen >

y^{''}+2y^'+2y=3,y(0)=1,y^'(0)=0

Lösung

y^{^{''}} + 2 y^{^{'}} + 2 y = 3, y (0) = 1, y^{^{'}} (0) = 0

Lösung

y = e^{- t} (- \frac{1}{2} cos (t) - \frac{1}{2} sin (t)) + \frac{3}{2}

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) + 2 y = 3

Solve linear ODE:

y = e^{- t} (- \frac{1}{2} cos (t) - \frac{1}{2} sin (t)) + \frac{3}{2}

y = e^{- t} (- \frac{1}{2} cos (t) - \frac{1}{2} sin (t)) + \frac{3}{2}

Graph

Beliebte Beispiele

y^{''}+5y^'+6y=e^{-x}

y^{^{''}} + 5 y^{^{'}} + 6 y = e^{- x}

(4d^2+12d+9)y=2022

(4 d^{2} + 12 d + 9) y = 2022

y^{''''}-y=3x+cos(x)

y^{^{''''}} - y = 3 x + cos (x)

y^{''}+3y^'+2y=u_{2}(t),y(0)=5,y^'(0)=3

y^{^{''}} + 3 y^{^{'}} + 2 y = u_{2} (t), y (0) = 5, y^{^{'}} (0) = 3

(D^2-D)y=e^xsin(x)

(D^{2} - D) y = e^{x} sin (x)