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Beliebt Rechnen >

y^{''}+7y+12y=t^2e^{-3t}

Lösung

y^{^{''}} + 7 y + 12 y = t^{2} e^{- 3 t}

Lösung

y = c_{1} cos (19 t) + c_{2} sin (19 t) + \frac{e ^{- 3 t} t ^{2}}{28} + \frac{3 e ^{- 3 t} t}{196} + \frac{1}{1372} e^{- 3 t}

Schritte zur Lösung

y^{''} (t) + 7 y + 12 y = t^{2} e^{- 3 t}

Solve linear ODE:

y = c_{1} cos (19 t) + c_{2} sin (19 t) + \frac{e ^{- 3 t} t ^{2}}{28} + \frac{3 e ^{- 3 t} t}{196} + \frac{1}{1372} e^{- 3 t}

y = c_{1} cos (19 t) + c_{2} sin (19 t) + \frac{e ^{- 3 t} t ^{2}}{28} + \frac{3 e ^{- 3 t} t}{196} + \frac{1}{1372} e^{- 3 t}

Graph

Beliebte Beispiele

5y^{''}+88y^'+240y=82sin(6x)

5 y^{^{''}} + 88 y^{^{'}} + 240 y = 82 sin (6 x)

(d^2-4)y=e^{-3x}sin(e^{-x})

(d^{2} - 4) y = e^{- 3 x} sin (e^{- x})

(D^2-6D+9)y=1+x+x^2

(D^{2} - 6 D + 9) y = 1 + x + x^{2}

y^{''}+3y^'+13y=52,y(0)=2,y^'(0)=1

y^{^{''}} + 3 y^{^{'}} + 13 y = 52, y (0) = 2, y^{^{'}} (0) = 1

y^{''}+2y^'-3y=5e^{2x},y(0)=0,y^'(0)=5

y^{^{''}} + 2 y^{^{'}} - 3 y = 5 e^{2 x}, y (0) = 0, y^{^{'}} (0) = 5