x^{''}-4a^2x=0

Lösung

x^{^{''}} - 4 a^{2} x = 0

x = c_{1} e^{2 a t} + c_{2} e^{- 2 a t}

Schritte zur Lösung

x^{''} (t) - 4 a^{2} x = 0

Solve linear ODE:

x = c_{1} e^{2 a t} + c_{2} e^{- 2 a t}

x = c_{1} e^{2 a t} + c_{2} e^{- 2 a t}

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 10

y^{^{''''}} + 3 y^{^{'}} = 0

\frac{y ^{^{''}}}{y ^{^{'}}} = a

9 y^{^{''}} + 12 y^{^{'}} + 4 y = 0, y (0) = - 3, y^{^{'}} (0) = 0

y^{^{''}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = \frac{12}{5}