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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

y^{''} (x) + 2 y^{'} (x) + 2 y = e^{- x} \cdot 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^{''}+6y^'+5y=30

y^{^{''}} + 6 y^{^{'}} + 5 y = 30

4y^{''}-4y^'+y=80e^{t/2}

4 y^{^{''}} - 4 y^{^{'}} + y = 80 e^{\frac{t}{2}}

-2y^{''}+y=e^{-0.2x},y(0)=1,y^'(1)=-y(1)

- 2 y^{^{''}} + y = e^{- 0.2 x}, y (0) = 1, y^{^{'}} (1) = - y (1)

y^{''}-64y=sinh(8x)

y^{^{''}} - 64 y = sinh (8 x)

y^{''}-y^'-2y=-2x^3+x^2+4x+1

y^{^{''}} - y^{^{'}} - 2 y = - 2 x^{3} + x^{2} + 4 x + 1