y^{''}-5y^'=0,y(0)=7-7e^5,y(1)=0

Lösung

y^{^{''}} - 5 y^{^{'}} = 0, y (0) = 7 - 7 e^{5}, y (1) = 0

y = (7 - 7 e^{5} - \frac{- 7 e ^{5} + 7 e ^{10}}{- e ^{5} + 1}) e^{5 t} + \frac{- 7 e ^{5} + 7 e ^{10}}{- e ^{5} + 1}

Schritte zur Lösung

y^{''} (t) - 5 y^{'} (t) = 0

Solve linear ODE:

y = (7 - 7 e^{5} - \frac{- 7 e ^{5} + 7 e ^{10}}{- e ^{5} + 1}) e^{5 t} + \frac{- 7 e ^{5} + 7 e ^{10}}{- e ^{5} + 1}

y = (7 - 7 e^{5} - \frac{- 7 e ^{5} + 7 e ^{10}}{- e ^{5} + 1}) e^{5 t} + \frac{- 7 e ^{5} + 7 e ^{10}}{- e ^{5} + 1}

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

l in e a r y^{^{''}} + 3 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} + 5^{2} y = 0

y^{^{''}} + 6 y^{^{'}} + 13 y = 0, y (0) = 3

2 y^{^{''}} + 9 y^{^{'}} - 5 y = 0