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Beliebt Rechnen >

y^{''}+4y^'+5y=2e^{-4x},y(0)=2,y^'(0)=3

Lösung

y^{^{''}} + 4 y^{^{'}} + 5 y = 2 e^{- 4 x}, y (0) = 2, y^{^{'}} (0) = 3

Lösung

y = e^{- 2 x} (\frac{8}{5} cos (x) + \frac{39}{5} sin (x)) + \frac{2}{5} e^{- 4 x}

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 5 y = 2 e^{- 4 x}

Solve linear ODE:

y = e^{- 2 x} (\frac{8}{5} cos (x) + \frac{39}{5} sin (x)) + \frac{2}{5} e^{- 4 x}

y = e^{- 2 x} (\frac{8}{5} cos (x) + \frac{39}{5} sin (x)) + \frac{2}{5} e^{- 4 x}

Graph

Beliebte Beispiele

y^{''}-2y^'-3y=e^6cos(t)

y^{^{''}} - 2 y^{^{'}} - 3 y = e^{6} cos (t)

(d^2+3d+2)y=1+3x+x^2

(d^{2} + 3 d + 2) y = 1 + 3 x + x^{2}

x^{''}+3x^'-4x=-4t+3

x^{^{''}} + 3 x^{^{'}} - 4 x = - 4 t + 3

y^{''}-4y^'+4=sin(x)

y^{^{''}} - 4 y^{^{'}} + 4 = sin (x)

y^{''}+2y^'=4,y(0)=3,y^'(0)=5

y^{^{''}} + 2 y^{^{'}} = 4, y (0) = 3, y^{^{'}} (0) = 5