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Beliebt Rechnen >

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

Lösung

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

Lösung

y = - \frac{1}{90} - \frac{1}{10} + \frac{1}{90} e^{- 9 t} + \frac{1}{10} e^{t}

Schritte zur Lösung

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

Solve linear ODE:

y = - \frac{1}{90} - \frac{1}{10} + \frac{1}{90} e^{- 9 t} + \frac{1}{10} e^{t}

y = - \frac{1}{90} - \frac{1}{10} + \frac{1}{90} e^{- 9 t} + \frac{1}{10} e^{t}

Graph

Beliebte Beispiele

y^{''}-4y^'+4y=2x-sin(2x)

y^{^{''}} - 4 y^{^{'}} + 4 y = 2 x - sin (2 x)

y^{''}-y=3xe^xcos(2x)

y^{^{''}} - y = 3 x e^{x} cos (2 x)

y^{''}+4y^'+5y=5

y^{^{''}} + 4 y^{^{'}} + 5 y = 5

4y^{''}+4y^'+y=(5e^{-t/2})/(t^2+1)

4 y^{^{''}} + 4 y^{^{'}} + y = \frac{5 e ^{- \frac{t}{2}}}{t ^{2} + 1}

y^{''}-5y^'+6y=-3sin(2x)

y^{^{''}} - 5 y^{^{'}} + 6 y = - 3 sin (2 x)