y^{''}-4y^'=0,y(0)=6-6e^4,y(1)=0

Lösung

y^{^{''}} - 4 y^{^{'}} = 0, y (0) = 6 - 6 e^{4}, y (1) = 0

y = (6 - 6 e^{4} - \frac{- 6 e ^{4} + 6 e ^{8}}{- e ^{4} + 1}) e^{4 t} + \frac{- 6 e ^{4} + 6 e ^{8}}{- e ^{4} + 1}

Schritte zur Lösung

y^{''} (t) - 4 y^{'} (t) = 0

Solve linear ODE:

y = (6 - 6 e^{4} - \frac{- 6 e ^{4} + 6 e ^{8}}{- e ^{4} + 1}) e^{4 t} + \frac{- 6 e ^{4} + 6 e ^{8}}{- e ^{4} + 1}

y = (6 - 6 e^{4} - \frac{- 6 e ^{4} + 6 e ^{8}}{- e ^{4} + 1}) e^{4 t} + \frac{- 6 e ^{4} + 6 e ^{8}}{- e ^{4} + 1}

y^{^{''}} - \frac{3}{2} y^{^{'}} - y = 0

y^{^{'''}} + 12 y^{^{''}} + 45 y^{^{'}} = 0

y^{^{''}} + 4 y = 0, y (\frac{π}{6}) = 4, y^{^{'}} (\frac{π}{6}) = - 8

y^{^{''}} - 8 y^{^{'}} = 20 y, y (0) = 0, y^{^{'}} (0) = 0

y^{^{'''}} - 3 y^{^{''}} - 9 y^{^{'}} - 5 y = 0