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Beliebt Rechnen >

x^{''''}+2x^{''}+x=4te^t

Lösung

x^{^{''''}} + 2 x^{^{''}} + x = 4 t e^{t}

Lösung

x = c_{1} cos (t) + c_{2} sin (t) + t (c_{3} cos (t) + c_{4} sin (t)) + e^{t} t - 2 e^{t}

Schritte zur Lösung

x^{(4)} (t) + 2 x^{''} (t) + x = 4 t e^{t}

Solve linear ODE:

x = c_{1} cos (t) + c_{2} sin (t) + t (c_{3} cos (t) + c_{4} sin (t)) + e^{t} t - 2 e^{t}

x = c_{1} cos (t) + c_{2} sin (t) + t (c_{3} cos (t) + c_{4} sin (t)) + e^{t} t - 2 e^{t}

Graph

Beliebte Beispiele

2y^{''}+3y^'+3y=e^{-3x}

2 y^{^{''}} + 3 y^{^{'}} + 3 y = e^{- 3 x}

2y^{''}-7y^'+3y=4x^2

2 y^{^{''}} - 7 y^{^{'}} + 3 y = 4 x^{2}

y^{''}+3y^'+2y=(1+e^{2x})^{-1}

y^{^{''}} + 3 y^{^{'}} + 2 y = (1 + e^{2 x})^{- 1}

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

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

y^{''}+4y^'+5y=35e^{(-4x)}

y^{^{''}} + 4 y^{^{'}} + 5 y = 35 e^{(- 4 x)}