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Beliebt Rechnen >

y^{''}+5y^'+6y=1,y(0)=1,y^'(0)=0

Lösung

y^{^{''}} + 5 y^{^{'}} + 6 y = 1, y (0) = 1, y^{^{'}} (0) = 0

Lösung

y = (\frac{5}{3} + \frac{5}{6}) e^{- 2 t} - \frac{5}{3} e^{- 3 t} + \frac{1}{6}

Schritte zur Lösung

y^{''} (t) + 5 y^{'} (t) + 6 y = 1

Solve linear ODE:

y = (\frac{5}{3} + \frac{5}{6}) e^{- 2 t} - \frac{5}{3} e^{- 3 t} + \frac{1}{6}

y = (\frac{5}{3} + \frac{5}{6}) e^{- 2 t} - \frac{5}{3} e^{- 3 t} + \frac{1}{6}

Graph

Beliebte Beispiele

y^{''}+25y=17sec^2(5t)

y^{^{''}} + 25 y = 17 sec^{2} (5 t)

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

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

y^{''}-16y^'+64y=2e^{8x}

y^{^{''}} - 16 y^{^{'}} + 64 y = 2 e^{8 x}

y^{''}+4y=16t,y^0=3,y^'0=-6

y^{^{''}} + 4 y = 16 t, y^{0} = 3, y^{^{'}} 0 = - 6

y^{''}+3y^'+2y=e^{-2x}+x^2

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{- 2 x} + x^{2}