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Beliebt Rechnen >

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

Lösung

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

Lösung

y = e^{- \frac{2 x}{5}} (c_{1} cos (\frac{4 x}{5}) + c_{2} sin (\frac{4 x}{5})) + \frac{35}{68} e^{- 4 x}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{- \frac{2 x}{5}} (c_{1} cos (\frac{4 x}{5}) + c_{2} sin (\frac{4 x}{5})) + \frac{35}{68} e^{- 4 x}

y = e^{- \frac{2 x}{5}} (c_{1} cos (\frac{4 x}{5}) + c_{2} sin (\frac{4 x}{5})) + \frac{35}{68} e^{- 4 x}

Graph

Beliebte Beispiele

y^{'''}+y^'=xsin(x+1)

y^{^{'''}} + y^{^{'}} = x sin (x + 1)

y^{''}+3y^'+4=0

y^{^{''}} + 3 y^{^{'}} + 4 = 0

y^{''}+9y=3sec^3(3x)

y^{^{''}} + 9 y = 3 sec^{3} (3 x)

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

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

y^{''}+(-3)y^'+4y=16x-12e^{2x}

y^{^{''}} + (- 3) y^{^{'}} + 4 y = 16 x - 12 e^{2 x}