y^{''}+12y^'+36y=0,y(0)=-2,y^'(0)=16

Lösung

y^{^{''}} + 12 y^{^{'}} + 36 y = 0, y (0) = - 2, y^{^{'}} (0) = 16

y = - 2 e^{- 6 t} + 4 e^{- 6 t} t

Schritte zur Lösung

y^{''} (t) + 12 y^{'} (t) + 36 y = 0

Solve linear ODE:

y = - 2 e^{- 6 t} + 4 e^{- 6 t} t

y = - 2 e^{- 6 t} + 4 e^{- 6 t} t

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

y^{^{''}} + 12 y^{^{'}} + 16 y = 0

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

\frac{d ^{2} y}{d x ^{2}} + 16 \frac{d y}{d x} + 64 y = 0

y^{^{''}} + 14 y^{^{'}} + 64 y = 0, y (0) = 5, y^{^{'}} (0) = 0