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Beliebt Rechnen >

3x^{''}+22x^'+48x=5cos(4t)

Lösung

3 x^{^{''}} + 22 x^{^{'}} + 48 x = 5 cos (4 t)

Lösung

x = e^{- \frac{11 t}{3}} (c_{1} cos (\frac{23 t}{3}) + c_{2} sin (\frac{23 t}{3})) + \frac{5}{88} sin (4 t)

Schritte zur Lösung

3 x^{''} (t) + 22 x^{'} (t) + 48 x = 5 cos (4 t)

Solve linear ODE:

x = e^{- \frac{11 t}{3}} (c_{1} cos (\frac{23 t}{3}) + c_{2} sin (\frac{23 t}{3})) + \frac{5}{88} sin (4 t)

x = e^{- \frac{11 t}{3}} (c_{1} cos (\frac{23 t}{3}) + c_{2} sin (\frac{23 t}{3})) + \frac{5}{88} sin (4 t)

Graph

Beliebte Beispiele

y^{''}-4y^'=x*e^{4x}

y^{^{''}} - 4 y^{^{'}} = x \cdot e^{4 x}

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

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

(d^2-6d+3)y=e^3x

(d^{2} - 6 d + 3) y = e^{3} x

y^{''}+4y^'+3y=6

y^{^{''}} + 4 y^{^{'}} + 3 y = 6

y^{''}+4y=1,6ty(0)=3,y^'(0)=-6

y^{^{''}} + 4 y = 1, 6 t y (0) = 3, y^{^{'}} (0) = - 6