y^{''}+2y^'+y=0,y^'0=-2

Lösung

y^{^{''}} + 2 y^{^{'}} + y = 0, y^{^{'}} 0 = - 2

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

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) + y = 0

Solve linear ODE:

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

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

y^{^{''}} + \frac{10}{3} y^{^{'}} + a y = 0, y (0) = 1, y^{^{'}} (0) = \frac{5}{3}

u^{^{''}} + u^{^{'}} = 0

9 y^{^{''}} - 30 y^{^{'}} - 24 y = 0, y (0) = 0, y^{^{'}} (0) = 1

\frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} + 6 y = 0

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = 5, y^{^{''}} (0) = 13