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Beliebt Rechnen >

y^{''}+4y^'+5y=-5x+3e^{(-x)}

Lösung

y^{^{''}} + 4 y^{^{'}} + 5 y = - 5 x + 3 e^{(- x)}

Lösung

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) - x + \frac{4}{5} + \frac{3}{2} e^{- x}

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 5 y = - 5 x + 3 e^{(- x)}

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) - x + \frac{4}{5} + \frac{3}{2} e^{- x}

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) - x + \frac{4}{5} + \frac{3}{2} e^{- x}

Graph

Beliebte Beispiele

y^{''}-3y^'+2y=11e^3x,y^1(0)=ex

y^{^{''}} - 3 y^{^{'}} + 2 y = 11 e^{3} x, y^{1} (0) = e x

y^{''}+4y=8x^2+7x

y^{^{''}} + 4 y = 8 x^{2} + 7 x

y^{^{''}} - 4 y^{^{'}} = x

y^{''}+3y=cos(sqrt(3)x)

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

y^{''}-4y^'=e^{4x}

y^{^{''}} - 4 y^{^{'}} = e^{4 x}