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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (0) = 4, y^{^{'}} (0) = - 6

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + y^{^{'}} - 6 y = 0, y (1) = 2 e^{2} - e^{- 3}

(D^{3} - 3 D^{2} + 3 D - 1) y = 0

8 y^{^{''}} - 9 y^{^{'}} + y = 0