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Beliebt Rechnen >

y^{''}+6y^'+9y=t

Lösung

y^{^{''}} + 6 y^{^{'}} + 9 y = t

Lösung

y = c_{1} e^{- 3 t} + c_{2} t e^{- 3 t} + \frac{t}{9} - \frac{2}{27}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- 3 t} + c_{2} t e^{- 3 t} + \frac{t}{9} - \frac{2}{27}

y = c_{1} e^{- 3 t} + c_{2} t e^{- 3 t} + \frac{t}{9} - \frac{2}{27}

Graph

Beliebte Beispiele

y^{''}-y=5e^{4t}+6te^{4t}+3t^2e^{4t}

y^{^{''}} - y = 5 e^{4 t} + 6 t e^{4 t} + 3 t^{2} e^{4 t}

y^{''}+42y=42cos(42t)

y^{^{''}} + 42 y = 42 cos (42 t)

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

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

y^{''}+2y^'+5y=e^xsin(x)

y^{^{''}} + 2 y^{^{'}} + 5 y = e^{x} sin (x)

y^{''}+y= 1/(sin^2(x))

y^{^{''}} + y = \frac{1}{sin ^{2} ( x )}