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Beliebt Rechnen >

x^{''}+2x^'+5x=e^t

Lösung

x^{^{''}} + 2 x^{^{'}} + 5 x = e^{t}

Lösung

x = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{1}{8} e^{t}

Schritte zur Lösung

x^{''} (t) + 2 x^{'} (t) + 5 x = e^{t}

Solve linear ODE:

x = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{1}{8} e^{t}

x = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{1}{8} e^{t}

Graph

Beliebte Beispiele

y^{''}+40y^'+4000y=800sin(40x)

y^{^{''}} + 40 y^{^{'}} + 4000 y = 800 sin (40 x)

y^{''}+y^'=e^xcos(x)

y^{^{''}} + y^{^{'}} = e^{x} cos (x)

(d-1)^3y=e^x+5^x-1

(d - 1)^{3} y = e^{x} + 5^{x} - 1

y^{''}-2y^'+y=12e^{3t},y(0)=-1,y^'(0)=0

y^{^{''}} - 2 y^{^{'}} + y = 12 e^{3 t}, y (0) = - 1, y^{^{'}} (0) = 0

2y^{''}-4y^'+2y=e^xx^{-1}

2 y^{^{''}} - 4 y^{^{'}} + 2 y = e^{x} x^{- 1}