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Beliebt Rechnen >

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

Lösung

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

Lösung

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

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

Graph

Beliebte Beispiele

y^{''}-y=xe^{x/2}

y^{^{''}} - y = x e^{\frac{x}{2}}

y^{''}+9y=e^{2x}+x^2sin(x)

y^{^{''}} + 9 y = e^{2 x} + x^{2} sin (x)

y^{''}+6y^'+8y=2t+e^t

y^{^{''}} + 6 y^{^{'}} + 8 y = 2 t + e^{t}

x^{''}+25x=2cos(5.1t)

x^{^{''}} + 25 x = 2 cos (5.1 t)

y^{'''}+9y^{''}+27y^'+27y=9e^{-3x}

y^{^{'''}} + 9 y^{^{''}} + 27 y^{^{'}} + 27 y = 9 e^{- 3 x}