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

Lösung

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

y = c_{1} e^{2 (3 - 1) t} + c_{2} e^{- 2 (1 + 3) t}

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) - 8 y = 0

Solve linear ODE:

y = c_{1} e^{2 (3 - 1) t} + c_{2} e^{- 2 (1 + 3) t}

y = c_{1} e^{2 (3 - 1) t} + c_{2} e^{- 2 (1 + 3) t}

y^{^{''}} + 5 y^{^{'}} = 0, y (0) = 9, y^{^{'}} (0) = - 20

\frac{d ^{2} x}{d t ^{2}} + 6 \cdot \frac{d x}{d t} + 3 \cdot x = 0, x (0) = 0

4 (\frac{d ^{2} y}{d x ^{2}}) + 4 (\frac{d y}{d x}) + y = 0

2500 y^{^{''}} + 81 y = 0

y^{^{''}} + 5 y^{^{'}} - 24 y = 0, y (0) = x, y^{^{'}} (0) = 56