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Beliebt Rechnen >

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

Lösung

2 \cdot y + 2 \cdot y^{^{'}} + y^{^{''}} = e^{- x} cos (x)

Lösung

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

Schritte zur Lösung

2 \cdot y + 2 \cdot y^{'} (x) + y^{''} (x) = e^{- x} cos (x)

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}-y^'=1,y(0)=18,y^'(0)=1

y^{^{''}} - y^{^{'}} = 1, y (0) = 18, y^{^{'}} (0) = 1

y^{^{''}} + 5 y = (x)

x^{''}-16x^'+64x=5te^{8t}

x^{^{''}} - 16 x^{^{'}} + 64 x = 5 t e^{8 t}

y^{''}-5y^'+6y=-2x+1

y^{^{''}} - 5 y^{^{'}} + 6 y = - 2 x + 1

0.05y^{''}+5y^'+1/(0.006)y=5sin(25x)

0.05 y^{^{''}} + 5 y^{^{'}} + \frac{1}{0.006} y = 5 sin (25 x)