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

Lösung

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

y = (4 - 4 e^{6} - \frac{- 4 e ^{6} + 4 e ^{12}}{- e ^{6} + 1}) e^{6 t} + \frac{- 4 e ^{6} + 4 e ^{12}}{- e ^{6} + 1}

Schritte zur Lösung

y^{''} (t) - 6 y^{'} (t) = 0

Solve linear ODE:

y = (4 - 4 e^{6} - \frac{- 4 e ^{6} + 4 e ^{12}}{- e ^{6} + 1}) e^{6 t} + \frac{- 4 e ^{6} + 4 e ^{12}}{- e ^{6} + 1}

y = (4 - 4 e^{6} - \frac{- 4 e ^{6} + 4 e ^{12}}{- e ^{6} + 1}) e^{6 t} + \frac{- 4 e ^{6} + 4 e ^{12}}{- e ^{6} + 1}

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

x^{^{''}} + 4 k^{2} x = 0

y^{^{''}} + y^{^{'}} + y = 0, y (0) = 0, y^{^{'}} (0) = 0

x^{^{''}} + 6 x^{^{'}} + 8 x = 0

4 y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = 1, y^{^{'}} (0) = 5