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Beliebt Rechnen >

y^{''}+5y^'+6y=24e^t+36t^2

Lösung

y^{^{''}} + 5 y^{^{'}} + 6 y = 24 e^{t} + 36 t^{2}

Lösung

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + 2 e^{t} + 6 t^{2} - 10 t + \frac{19}{3}

Schritte zur Lösung

y^{''} (t) + 5 y^{'} (t) + 6 y = 24 e^{t} + 36 t^{2}

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + 2 e^{t} + 6 t^{2} - 10 t + \frac{19}{3}

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + 2 e^{t} + 6 t^{2} - 10 t + \frac{19}{3}

Graph

Beliebte Beispiele

y^{''}-2y^'+2=0

y^{^{''}} - 2 y^{^{'}} + 2 = 0

y^{''}-2y^'-3y=5e^{4x},y(0)=1,y^'(0)=0

y^{^{''}} - 2 y^{^{'}} - 3 y = 5 e^{4 x}, y (0) = 1, y^{^{'}} (0) = 0

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

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

y^{''}-y=2,y(0)=2,y^'(0)=0

y^{^{''}} - y = 2, y (0) = 2, y^{^{'}} (0) = 0

y^{''}+4y=4sec^2(2t)

y^{^{''}} + 4 y = 4 sec^{2} (2 t)