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

Lösung

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

y = (5 - 5 e^{4} - \frac{- 5 e ^{4} + 5 e ^{8}}{- e ^{4} + 1}) e^{4 t} + \frac{- 5 e ^{4} + 5 e ^{8}}{- e ^{4} + 1}

Schritte zur Lösung

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

Solve linear ODE:

y = (5 - 5 e^{4} - \frac{- 5 e ^{4} + 5 e ^{8}}{- e ^{4} + 1}) e^{4 t} + \frac{- 5 e ^{4} + 5 e ^{8}}{- e ^{4} + 1}

y = (5 - 5 e^{4} - \frac{- 5 e ^{4} + 5 e ^{8}}{- e ^{4} + 1}) e^{4 t} + \frac{- 5 e ^{4} + 5 e ^{8}}{- e ^{4} + 1}

4 y^{^{''}} + 7 y^{^{'}} + 8 y = 0

y^{^{''}} + 10 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} = 0

x^{^{''}} - 3 x^{^{'}} = 0

y^{^{''}} + 4 \cdot y^{^{'}} + 4 \cdot y = 0