y^{''}+200y^'+1000y=0

Lösung

y^{^{''}} + 200 y^{^{'}} + 1000 y = 0

y = c_{1} e^{10 (310 - 10) t} + c_{2} e^{- 10 (10 + 310) t}

Schritte zur Lösung

y^{''} (t) + 200 y^{'} (t) + 1000 y = 0

Solve linear ODE:

y = c_{1} e^{10 (310 - 10) t} + c_{2} e^{- 10 (10 + 310) t}

y = c_{1} e^{10 (310 - 10) t} + c_{2} e^{- 10 (10 + 310) t}

y^{^{''}} - 4^{2} y = 0

y^{^{''}} + 12 y^{^{'}} + 32 y = 0

\frac{d ^{2} x}{d t ^{2}} + \frac{53}{49} \frac{d x}{d t} + 49 x = 0

y^{^{''}} + 18 y^{^{'}} + 117 y = 0, y (0) = 6, y^{^{'}} (0) = 3

4 y^{^{'}} + 9 y^{^{''}} = - 5 y, y (0) = 2, y^{^{'}} (0) = 0