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Beliebt Rechnen >

y^{''}-y^'+14y=5+e^{x/2}

Lösung

y^{^{''}} - y^{^{'}} + 14 y = 5 + e^{\frac{x}{2}}

Lösung

y = e^{\frac{x}{2}} (c_{1} cos (\frac{5 5 ^{\frac{1}{2}} x}{2}) + c_{2} sin (\frac{5 5 ^{\frac{1}{2}} x}{2})) + \frac{5}{14} + \frac{4}{55} e^{\frac{x}{2}}

Schritte zur Lösung

y^{''} (x) - y^{'} (x) + 14 y = 5 + e^{\frac{x}{2}}

Solve linear ODE:

y = e^{\frac{x}{2}} (c_{1} cos (\frac{5 5 ^{\frac{1}{2}} x}{2}) + c_{2} sin (\frac{5 5 ^{\frac{1}{2}} x}{2})) + \frac{5}{14} + \frac{4}{55} e^{\frac{x}{2}}

y = e^{\frac{x}{2}} (c_{1} cos (\frac{5 5 ^{\frac{1}{2}} x}{2}) + c_{2} sin (\frac{5 5 ^{\frac{1}{2}} x}{2})) + \frac{5}{14} + \frac{4}{55} e^{\frac{x}{2}}

Graph

Beliebte Beispiele

y^{''}-16y=9.6e^{4x}+30e^x

y^{^{''}} - 16 y = 9.6 e^{4 x} + 30 e^{x}

y^{''}-y=3e^{2x}

y^{^{''}} - y = 3 e^{2 x}

y^{''}+y^'+y=13e^{-2t}(cos(t)+2sin(t))

y^{^{''}} + y^{^{'}} + y = 13 e^{- 2 t} (cos (t) + 2 sin (t))

y^{'''}+6y=7y^'+4e^x

y^{^{'''}} + 6 y = 7 y^{^{'}} + 4 e^{x}

y^{^{''}} + y - 12 = 0