y^{''}-7y^'=0,y(0)=2-2e^7,y(1)=0

Lösung

y^{^{''}} - 7 y^{^{'}} = 0, y (0) = 2 - 2 e^{7}, y (1) = 0

y = (2 - 2 e^{7} - \frac{- 2 e ^{7} + 2 e ^{14}}{- e ^{7} + 1}) e^{7 t} + \frac{- 2 e ^{7} + 2 e ^{14}}{- e ^{7} + 1}

Schritte zur Lösung

y^{''} (t) - 7 y^{'} (t) = 0

Solve linear ODE:

y = (2 - 2 e^{7} - \frac{- 2 e ^{7} + 2 e ^{14}}{- e ^{7} + 1}) e^{7 t} + \frac{- 2 e ^{7} + 2 e ^{14}}{- e ^{7} + 1}

y = (2 - 2 e^{7} - \frac{- 2 e ^{7} + 2 e ^{14}}{- e ^{7} + 1}) e^{7 t} + \frac{- 2 e ^{7} + 2 e ^{14}}{- e ^{7} + 1}

\frac{d ^{2} y}{d x ^{2}} + 15 \frac{d y}{d x} + 56 y = 0

y^{^{''}} + 4 y^{^{'}} + k y = 0

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

y^{^{''}} + 7 y^{^{'}} + 20 y = 0

2 y^{^{''}} + 14 y^{^{'}} + 12 y = 0, y (0) = 1, y^{^{'}} (0) = 0