1/4 y^{''}+sqrt(2)y^'+2y=0

Lösung

\frac{1}{4} y^{^{''}} + 2 y^{^{'}} + 2 y = 0

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

Schritte zur Lösung

\frac{1}{4} y^{''} (t) + 2 y^{'} (t) + 2 y = 0

Solve linear ODE:

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

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

4 y^{^{''}} - 16 y^{^{'}} + 17 y = 0

y^{^{''}} - 7 y^{^{'}} + 12 y = 0, y (0) = 0, y (0) = 3

y^{^{''}} + (a - 1) y^{^{'}} + b y = 0

8 y^{^{''}} - 9 y^{^{'}} + y = 0, y (0) = 8, y^{^{'}} (0) = \frac{1}{8}

y^{^{''''}} - 2 y^{^{'''}} - 10 y^{^{''}} + 6 y^{^{'}} + 45 y = 0