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Beliebt Rechnen >

3x^{''}+25x^'+48x=5cos(4t)

Lösung

3 x^{^{''}} + 25 x^{^{'}} + 48 x = 5 cos (4 t)

Lösung

x = c_{1} e^{- 3 t} + c_{2} e^{- \frac{16 t}{3}} + \frac{1}{20} sin (4 t)

Schritte zur Lösung

3 x^{''} (t) + 25 x^{'} (t) + 48 x = 5 cos (4 t)

Solve linear ODE:

x = c_{1} e^{- 3 t} + c_{2} e^{- \frac{16 t}{3}} + \frac{1}{20} sin (4 t)

x = c_{1} e^{- 3 t} + c_{2} e^{- \frac{16 t}{3}} + \frac{1}{20} sin (4 t)

Graph

Beliebte Beispiele

y^{''}+4y=t^2+6e^t,y(0)=0,y^'(0)=5

y^{^{''}} + 4 y = t^{2} + 6 e^{t}, y (0) = 0, y^{^{'}} (0) = 5

y^{''}-8y^'+20y=100x^2-39xe^x

y^{^{''}} - 8 y^{^{'}} + 20 y = 100 x^{2} - 39 x e^{x}

y^{''}-2y^'+2y=e^xcsc(x)

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{x} csc (x)

y^{''}+y=sin(3x)

y^{^{''}} + y = sin (3 x)

y^{'''}-6y^{''}+12y^'-8y=16e^{-2t}

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = 16 e^{- 2 t}