y^{''}+7y^'=0,y(0)=8,y^'(0)=-3

Lösung

y^{^{''}} + 7 y^{^{'}} = 0, y (0) = 8, y^{^{'}} (0) = - 3

y = 8 - \frac{3}{7} + \frac{3}{7} e^{- 7 t}

Schritte zur Lösung

y^{''} (t) + 7 y^{'} (t) = 0

Solve linear ODE:

y = 8 - \frac{3}{7} + \frac{3}{7} e^{- 7 t}

y = 8 - \frac{3}{7} + \frac{3}{7} e^{- 7 t}

y^{^{''}} - 2 y^{^{'}} - 3 y = 0, y^{^{'}} (0) = 4

36 \frac{d ^{2} y}{d x ^{2}} + 12 \frac{d y}{d x} + y = 0

y^{^{''}} + 6 y^{^{'}} + 8 y = 0, y (0) = - 1, y^{^{'}} (0) = 2

y^{^{''}} - 4 y + 13 y = 0

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 2, y^{^{'}} (0) = 4