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Beliebt Rechnen >

y^{''}+9y^'+14y= 1/2 sin(t)

Lösung

y^{^{''}} + 9 y^{^{'}} + 14 y = \frac{1}{2} sin (t)

Lösung

y = c_{1} e^{- 2 t} + c_{2} e^{- 7 t} + \frac{13}{500} sin (t) - \frac{9}{500} cos (t)

Schritte zur Lösung

y^{''} (t) + 9 y^{'} (t) + 14 y = \frac{1}{2} sin (t)

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 7 t} + \frac{13}{500} sin (t) - \frac{9}{500} cos (t)

y = c_{1} e^{- 2 t} + c_{2} e^{- 7 t} + \frac{13}{500} sin (t) - \frac{9}{500} cos (t)

Graph

Beliebte Beispiele

(D^2-4D+4)(y)=6x^2e^{2x}

(D^{2} - 4 D + 4) (y) = 6 x^{2} e^{2 x}

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

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

D (D - 3) y = 3 t + \frac{t}{2}

8y^{''}-6y^'+y=6cosh(x)

8 y^{^{''}} - 6 y^{^{'}} + y = 6 cosh (x)

y^{^{''}} - 100 y = 15