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Beliebt Rechnen >

y^{''}-2y^'+3y=3e^{2t}

Lösung

y^{^{''}} - 2 y^{^{'}} + 3 y = 3 e^{2 t}

Lösung

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

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) + 3 y = 3 e^{2 t}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}-4y^'+4y=e^{2t}ln(t)

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{2 t} ln (t)

y^{''}-7y^'+6y=x,y^1(0)=ex

y^{^{''}} - 7 y^{^{'}} + 6 y = x, y^{1} (0) = e x

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

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

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

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

y^{''}+2y^'+y=g(t-1),y(0)=2,y^'(0)=3

y^{^{''}} + 2 y^{^{'}} + y = g (t - 1), y (0) = 2, y^{^{'}} (0) = 3