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Beliebt Rechnen >

y^{''}+14y^'+49y=t-2e-7t

Lösung

y^{^{''}} + 14 y^{^{'}} + 49 y = t - 2 e - 7 t

Lösung

y = c_{1} e^{- 7 t} + c_{2} t e^{- 7 t} - \frac{6 t}{49} + \frac{- 14 e + 12}{343}

Schritte zur Lösung

y^{''} (t) + 14 y^{'} (t) + 49 y = t - 2 e - 7 t

Solve linear ODE:

y = c_{1} e^{- 7 t} + c_{2} t e^{- 7 t} - \frac{6 t}{49} + \frac{- 14 e + 12}{343}

y = c_{1} e^{- 7 t} + c_{2} t e^{- 7 t} - \frac{6 t}{49} + \frac{- 14 e + 12}{343}

Graph

Beliebte Beispiele

y^{''}+9y=(x^2+1)e^{3x}

y^{^{''}} + 9 y = (x^{2} + 1) e^{3 x}

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

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

3x^{''}+12x=sin(2t)

3 x^{^{''}} + 12 x = sin (2 t)

y^{'''}+2y^{''}=12x+4

y^{^{'''}} + 2 y^{^{''}} = 12 x + 4

y^{''}+25y=25sec^2(5t)

y^{^{''}} + 25 y = 25 sec^{2} (5 t)