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Beliebt Rechnen >

y^{''}+2y^'+2y=x^2+sin(x)

Lösung

y^{^{''}} + 2 y^{^{'}} + 2 y = x^{2} + sin (x)

Lösung

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

Schritte zur Lösung

y^{''} (x) + 2 y^{'} (x) + 2 y = x^{2} + sin (x)

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+3y^'-10y=3e^{-5x}

y^{^{''}} + 3 y^{^{'}} - 10 y = 3 e^{- 5 x}

y^{''}+10y^'+25y=(2+6x)e^{-5x}

y^{^{''}} + 10 y^{^{'}} + 25 y = (2 + 6 x) e^{- 5 x}

y^{''}+2y^'-y=-4

y^{^{''}} + 2 y^{^{'}} - y = - 4

y^{^{''}} - 16 y = 96

y^{''}-14y^'+49y=28x+6

y^{^{''}} - 14 y^{^{'}} + 49 y = 28 x + 6