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Beliebt Rechnen >

y^{''}-6y^'+9y=t,y(0)=0,y(0)=1

Lösung

y^{^{''}} - 6 y^{^{'}} + 9 y = t, y (0) = 0, y (0) = 1

Lösung

y = - \frac{2}{27} e^{3 t} + c_{2} e^{3 t} t + \frac{t}{9} + \frac{2}{27}

Schritte zur Lösung

y^{''} (t) - 6 y^{'} (t) + 9 y = t

Solve linear ODE:

y = - \frac{2}{27} e^{3 t} + c_{2} e^{3 t} t + \frac{t}{9} + \frac{2}{27}

y = - \frac{2}{27} e^{3 t} + c_{2} e^{3 t} t + \frac{t}{9} + \frac{2}{27}

Graph

Beliebte Beispiele

y^{''}-2y^'-3y=3x-4

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 x - 4

y^{''}+2y^'=2x+5+e^{-2x}

y^{^{''}} + 2 y^{^{'}} = 2 x + 5 + e^{- 2 x}

y^{'''}-4y^'=te^{-2t}+3cos(2t)

y^{^{'''}} - 4 y^{^{'}} = t e^{- 2 t} + 3 cos (2 t)

y^{''}+y^'=-8e^{-x}-4

y^{^{''}} + y^{^{'}} = - 8 e^{- x} - 4

x^{''}+2x^'+5x=12cos(2t)+3sin(2t)

x^{^{''}} + 2 x^{^{'}} + 5 x = 12 cos (2 t) + 3 sin (2 t)