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Beliebt Rechnen >

y^{''}-y^'-2y=0,y(0)=0,y(pi/2)=1

Lösung

y^{^{''}} - y^{^{'}} - 2 y = 0, y (0) = 0, y (\frac{π}{2}) = 1

Lösung

y = (e^{\frac{π}{2}} + \frac{e ^{\frac{π}{2}} + e ^{2 π}}{e ^{3 π} - 1}) e^{\frac{4 t - 3 π}{2}} - \frac{e ^{\frac{π}{2}} + e ^{2 π}}{e ^{3 π} - 1} e^{- t}

Schritte zur Lösung

y^{''} (t) - y^{'} (t) - 2 y = 0

Solve linear ODE:

y = (e^{\frac{π}{2}} + \frac{e ^{\frac{π}{2}} + e ^{2 π}}{e ^{3 π} - 1}) e^{\frac{4 t - 3 π}{2}} - \frac{e ^{\frac{π}{2}} + e ^{2 π}}{e ^{3 π} - 1} e^{- t}

y = (e^{\frac{π}{2}} + \frac{e ^{\frac{π}{2}} + e ^{2 π}}{e ^{3 π} - 1}) e^{\frac{4 t - 3 π}{2}} - \frac{e ^{\frac{π}{2}} + e ^{2 π}}{e ^{3 π} - 1} e^{- t}

Graph

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