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Beliebt Rechnen >

y^{''}+y^'+y=13e^{-2x}(cos(x)+2sin(x))

Lösung

y^{^{''}} + y^{^{'}} + y = 13 e^{- 2 x} (cos (x) + 2 sin (x))

Lösung

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) + e^{- 2 x} sin (x) + 8 e^{- 2 x} cos (x)

Schritte zur Lösung

y^{''} (x) + y^{'} (x) + y = 13 e^{- 2 x} (cos (x) + 2 sin (x))

Solve linear ODE:

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) + e^{- 2 x} sin (x) + 8 e^{- 2 x} cos (x)

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) + e^{- 2 x} sin (x) + 8 e^{- 2 x} cos (x)

Graph

Beliebte Beispiele

y^{''}+y^'=7,y(0)=1,y^'(0)=0

y^{^{''}} + y^{^{'}} = 7, y (0) = 1, y^{^{'}} (0) = 0

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

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

y^{''''}-y^{''}=2sin(t)-3e^{-t}+4t

y^{^{''''}} - y^{^{''}} = 2 sin (t) - 3 e^{- t} + 4 t

y^{''}+4y=cos(4t)+2sin(4t)

y^{^{''}} + 4 y = cos (4 t) + 2 sin (4 t)

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

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