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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{- t} + c_{2} e^{2 t} + \frac{1}{2} e^{t}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{2 t} + \frac{1}{2} e^{t}

y = c_{1} e^{- t} + c_{2} e^{2 t} + \frac{1}{2} e^{t}

Graph

Beliebte Beispiele

y^{''}-4y^'-21y=800e^{-t}

y^{^{''}} - 4 y^{^{'}} - 21 y = 800 e^{- t}

y^{''}+5y^'+4y=13te^{4t}

y^{^{''}} + 5 y^{^{'}} + 4 y = 13 t e^{4 t}

y^{''}-2y^'-8y=(x+1)e^x

y^{^{''}} - 2 y^{^{'}} - 8 y = (x + 1) e^{x}

y^{''}-y^'-6y=56cos(3x)

y^{^{''}} - y^{^{'}} - 6 y = 56 cos (3 x)

(d^2+6d+10)y=3e^{-3x}x-2e^{3x}cos(x)

(d^{2} + 6 d + 10) y = 3 e^{- 3 x} x - 2 e^{3 x} cos (x)