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Beliebt Rechnen >

y^{''}+y^'-6y=20e^t,y(0)=0,y^'(0)=1

Lösung

y^{^{''}} + y^{^{'}} - 6 y = 20 e^{t}, y (0) = 0, y^{^{'}} (0) = 1

Lösung

y = (- \frac{4}{5} + 5) e^{2 t} + \frac{4}{5} e^{- 3 t} - 5 e^{t}

Schritte zur Lösung

y^{''} (t) + y^{'} (t) - 6 y = 20 e^{t}

Solve linear ODE:

y = (- \frac{4}{5} + 5) e^{2 t} + \frac{4}{5} e^{- 3 t} - 5 e^{t}

y = (- \frac{4}{5} + 5) e^{2 t} + \frac{4}{5} e^{- 3 t} - 5 e^{t}

Graph

Beliebte Beispiele

2y^{''}+6y^'=10sin(7t)

2 y^{^{''}} + 6 y^{^{'}} = 10 sin (7 t)

y^{''}+4y=16t^3sin(2t)

y^{^{''}} + 4 y = 16 t^{3} sin (2 t)

y^{''}+11y^'+18y=5

y^{^{''}} + 11 y^{^{'}} + 18 y = 5

y^{''}-y^'+14y=2+e^{x/2}

y^{^{''}} - y^{^{'}} + 14 y = 2 + e^{\frac{x}{2}}

y^{''}+4y=t^2sin(2t)+(6t+7)cos(2t)

y^{^{''}} + 4 y = t^{2} sin (2 t) + (6 t + 7) cos (2 t)