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Beliebt Rechnen >

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

Lösung

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

Lösung

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{7 x}{2}) + c_{2} sin (\frac{7 x}{2})) + \frac{1}{4} e^{x}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{7 x}{2}) + c_{2} sin (\frac{7 x}{2})) + \frac{1}{4} e^{x}

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{7 x}{2}) + c_{2} sin (\frac{7 x}{2})) + \frac{1}{4} e^{x}

Graph

Beliebte Beispiele

y^{''}+2y=e^{-2x}(x^2+1)

y^{^{''}} + 2 y = e^{- 2 x} (x^{2} + 1)

y^{''}+2y^'+y=g(t-1),y(0)=2,y^'(0)=3

y^{^{''}} + 2 y^{^{'}} + y = g (t - 1), y (0) = 2, y^{^{'}} (0) = 3

y^{''}+4y=t^2+4e^t

y^{^{''}} + 4 y = t^{2} + 4 e^{t}

y^{''}+2y=12sin(2t),y(0)=5

y^{^{''}} + 2 y = 12 sin (2 t), y (0) = 5

y^{''}+y^'-2y=3e^{-2t},y(0)=2,y^'(0)=1

y^{^{''}} + y^{^{'}} - 2 y = 3 e^{- 2 t}, y (0) = 2, y^{^{'}} (0) = 1