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Beliebt Rechnen >

x^{''}+6x^'+23x=8cos(4t)

Lösung

x^{^{''}} + 6 x^{^{'}} + 23 x = 8 cos (4 t)

Lösung

x = e^{- 3 t} (c_{1} cos (14 t) + c_{2} sin (14 t)) + \frac{192}{625} sin (4 t) + \frac{56}{625} cos (4 t)

Schritte zur Lösung

x^{''} (t) + 6 x^{'} (t) + 23 x = 8 cos (4 t)

Solve linear ODE:

x = e^{- 3 t} (c_{1} cos (14 t) + c_{2} sin (14 t)) + \frac{192}{625} sin (4 t) + \frac{56}{625} cos (4 t)

x = e^{- 3 t} (c_{1} cos (14 t) + c_{2} sin (14 t)) + \frac{192}{625} sin (4 t) + \frac{56}{625} cos (4 t)

Graph

Beliebte Beispiele

y^{''}-7y^'+12y=4e^x

y^{^{''}} - 7 y^{^{'}} + 12 y = 4 e^{x}

4y^{''}+36y=csc(x)

4 y^{^{''}} + 36 y = csc (x)

y^{''}-2y^'+y=xe^x+4,y(0)=1,y^'(0)=1

y^{^{''}} - 2 y^{^{'}} + y = x e^{x} + 4, y (0) = 1, y^{^{'}} (0) = 1

y^{''}-6y=u^2(t),y(0)=0

y^{^{''}} - 6 y = u^{2} (t), y (0) = 0

y^{''}+16y=e^{5t}

y^{^{''}} + 16 y = e^{5 t}