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Beliebt Rechnen >

y^{''}+4y^'+5y=4+12t-5t^2

Lösung

y^{^{''}} + 4 y^{^{'}} + 5 y = 4 + 12 t - 5 t^{2}

Lösung

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

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) + 5 y = 4 + 12 t - 5 t^{2}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+7y^'=196sin(7t)+588cos(7t)

y^{^{''}} + 7 y^{^{'}} = 196 sin (7 t) + 588 cos (7 t)

x^{''}+49x=96cos(5t)

x^{^{''}} + 49 x = 96 cos (5 t)

(d^2y)/(dx^2)-y=xe^{2x}

\frac{d ^{2} y}{d x ^{2}} - y = x e^{2 x}

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

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

y^{''}+5y^'+4y=8x

y^{^{''}} + 5 y^{^{'}} + 4 y = 8 x