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Beliebt Rechnen >

y^{''}-2y^'+5y=20sin(t)

Lösung

y^{^{''}} - 2 y^{^{'}} + 5 y = 20 sin (t)

Lösung

y = e^{t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + 4 sin (t) + 2 cos (t)

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) + 5 y = 20 sin (t)

Solve linear ODE:

y = e^{t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + 4 sin (t) + 2 cos (t)

y = e^{t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + 4 sin (t) + 2 cos (t)

Graph

Beliebte Beispiele

y^{''}-2y^'-3y=6x+4

y^{^{''}} - 2 y^{^{'}} - 3 y = 6 x + 4

y^{''}+4y=6sin(2t),y(0)=2,y^'(0)=1

y^{^{''}} + 4 y = 6 sin (2 t), y (0) = 2, y^{^{'}} (0) = 1

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

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

y^{''}+y^'-2y=13+e^x

y^{^{''}} + y^{^{'}} - 2 y = 13 + e^{x}

y^{''}-3y^'-4y=4t^2-1

y^{^{''}} - 3 y^{^{'}} - 4 y = 4 t^{2} - 1