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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}-2y^'+10y=40,y(0)=0,y^'(0)=0

y^{^{''}} - 2 y^{^{'}} + 10 y = 40, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 4 \cdot y = - 3

u^{''}-a*\H(x)=x

u^{^{''}} - a \cdot H (x) = x

x^{''}+5x^'+4x=t+1

x^{^{''}} + 5 x^{^{'}} + 4 x = t + 1

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

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